If you were a Japanese citizen with a boatload of Yen stashed in your bank account after 1931, you'd want to get rid of it as soon as possible! Throughout the entirety of the pre-1945 period, Japan suffered chronic balance of payments problems owing to the cheapness of its main exports (usually textiles) and the cost of importing foreign technology. Japan was the first country following the 1929 market crash to institute a "gold embargo", prohibiting the export of gold (which then backed the Yen), and the first major power to leave the gold standard entirely. Though this (and the subsequent monetary expansion) had a stabilizing effect on the Japanese economy, which grew by around 50% in the first four years of the depression while the rest of the world shrank, it led to a devaluation of the currency abroad and double-digit inflation at home - a persistent problem which continued until the end of WW2.

As for the nature of the colonial currencies, with the exception of the Manchukuo Yuan they were de facto no currencies at all. Both early Japanese colonies (Korea and Taiwan) were governed along the French model, which included having separate colonial currencies pegged to that of the metropole. These currencies were echangeable at fixed rates maintained by the foreign currency reserves (meaning, at the time, the gold reserves) of the colonial overlord. For the balance sheet of Japan's financial bureaucracy, earning Korean yen through export was in no way equivalent to earning US dollars or French francs. Earnings of Korean yen could not meaningfully contribute to Japan's foreign exchange reserves since Japan's own gold and foreign currency reserves were required to stabilize the Korean yen's exchange rate. This may all sound arcane, so in simpler terms: a currency, especially in the age of the gold standard, was only as good as its backer. In the case of the Korean yen, Taiwanese yen, and Japanese yen, the backer was the same.

This all begs the question of why the Japanese - and their French models - bothered to create separate currencies in the first place, and the answer is control. It was far easier for non-Japanese to acquire Japanese yen than Taiwanese or Korean yen, especially because Japan was still subject to unequal treaties that restricted its trade policy until 1911. The Japanese, moreso than any other colonial power, demanded that their colonies operate at a profit. This was explicitly written into the bylaws and charters of many colonial governments and corporations. Profits in all Japan's colonies were largely buoyed by the opium trade, so it was imperative that the British, French, and Americans were kept out of this trade. This was much easier to do through the creation of a parallel currency that was only exchanged only to Japanese businesses affiliated with the colonial authorities, giving them a monopoly on the lucrative drug trade. Separate currencies also ensured colonial governments could limit the amount of capital that entered the colonies. If "too much" capital entered, Korean and Taiwanese wages would increase, decreasing the profits of businesses affiliated with the colonial governments.

Manchukuo was the exception. Following Chinese tradition, Manchukuo's currency existed on the silver standard until 1935. The independence of the Manchukuo currency was related to the relative independence of Manchukuo as a whole. Manchukuo was created by an act of mutiny: then-colonel Kanji Ishiwara faked a Chinese bomb attack on the Japanese-owned South Manchuria Railway, commencing hostilities without orders. The Japanese army followed a Prussian system of decentralized command, which allowed countless other officers to follow suit without orders from their seniors, which forced Tokyo to accept the "fait accompli" of the Manchurian war. In the aftermath of the "Mukden Incident", Manchuria became the private project of three men: Tojo Hideki, Inspector General of the Kantogun (the army formation guarding the South Manchuria Railway), Matsuoka Yosuke, President of the South Manchuria Railway, and Kishi Nobusuke, heir to the throne of the Ministry of Commerce and Industry. The "troika" of Manchuria were all leaders of the "reformist" faction within Japanese politics which sponsored Soviet-style industrialization of a still-agrarian Japan, and were enemies of the "mainstream" of Japanese politics: pork-barrel party bosses, zaibatsu (large, family-owned trading companies), and generals who clung to Japan's traditional doctrine emphasizing "fighting spirit".

Naturally, the troika preferred to keep as much administrative distance between themselves and Tokyo as possible, preserving their own currency and only inviting zaibatsu who agreed with them (the largest of which, Nissan, flatteringly renamed itself "Manchurian Industrial Development Corporation"). This was only possible because of Manchuria's inherent power - at the time of the Mukden Incident, Manchuria constituted 90% of China's industry, and, following the troika's industrialization campaign, matched the GDP of Japan itself. The division of Manchukuo from Japan was accentuated by the polarization of the Tokyo and Hsinking bureaucracies. Between 1931 and 1936, the Japanese Empire was effectively "split" in two as conservatives in Tokyo exiled reformist bureaucrats and military officers to Manchuria, culminating in the exile of Kishi himself in 1936.

The gradual resolution of this split had consequences for Manchuria's currency. In 1931, the reformists earned a rare victory in the appointment of Takahashi Korekiyo as Minister of Finance, reshaping what was once the most conservative ministry. Korekiyo implemented a proto-Keynesian fiscal policy and an expansionary monetary policy before Keynes had authored the General Theory. Korekiyo remained the only cabinet-level minister with whom the troika had good relations, so they agreed to his request to dismantle the Manchukuo silver standard in 1935 and peg the Yuan to the yen like Japan's other colonial currencies. This did not change the fact, however, that the troika were in control of Manchukuo's foreign currency stock and could selectively admit or deny foreign investment and monopolize the drug trade.

Because of the restrictive intention of colonial currencies, acquiring a significant amount of them was not a simple business. For a Japanese citizen, Korean and Taiwanese yen could be most easily acquired at the Yokohama Specie Bank, which throughout the period was the Japanese government's main front for colonial businesses. A more specific institution like the Taiwan Development Bank could also provide you with currency, but these banks were set up to cater to special interests already in the colony instead of the Tokyo government: in other words, if you had no affiliation to the colonial governments, you were better off avoiding the development banks. If you were well connected, you could acquire colonial yen directly from the Bank of Chosen or the Bank of Taiwan, but these institutions existed primarily issue and distribute the currency along existing distribution channels (i,e. the bureaucracies of the colonial government and affiliated businesses) and they placed no emphasis on "new customer"-facing interaction. In short, if you wanted to acquire a large amount of colonial yen, a visit to the Yokohama Specie Bank was your best bet. You would be briefly interrogated as to what you intended to do with colonial cash, the tellers would, depending on the year, telegram or call someone in the colonial office, and your business venture (or exceedingly expensive travel plan) would be approved or denied.

Problematically, all this had to happen beforehand. There were no YSB branches in Korea or Taiwan (even though there were in Shanghai, Dalian, and Honolulu). Also for this reason, you had exactly no chance of making use of your extensive yen savings at home.

An expensive visit to Manchuria was a more complicated affair. There was a YSB branch in Dalian, so theoretically you could convert currencies after arriving in Manchuria, but your chances of doing this were slim - even if (no, especially if) you were an eminent member of Japan's establishment. As mentioned, Kishi wanted no zaibatsu in Manchukuo except those who agreed with state-led development, and his close relationship with Nissan founder Aikawa Yoshisuke ensured that any development project that even remotely competed with a Nissan interest would be shot down on arrival. A visit to the Dalian branch of the YSB after 1931 would likely provoke an visit to your lodgings by an officer of the Kantogun, who would grill you on exactly what you were planning to do in Manchukuo with such a large sum of money and remind you that this was not a country for zaibatsu buchō like you.

As for the military yen, this was strictly a method of "legalized plunder". By law, many occupied territories in WW2 had to conduct business in military yen. The Japanese military received however much military yen it needed, and these were used to "buy" needed local products like provisions and civilian labor. Military yen could not be exchanged for Japanese yen, unlike the other colonial currencies.

Sources:

Johnson, Chalmers. MITI and the Japanese Boom.

Driscoll, Mark. Absolute Erotic, Absolute Grotesque: The Living, Dead, and Undead in Japanese Imperialism.

Daba, Hiroshi. Gotō Shinpei o meguru.

Fletcher, William Miles. The Japanese Business Community and National Trade Policy, 1920–1942.

Duus, Peter. The Abacus and the Sword: the Japanese Penetration of Korea, 1895–1910.