It almost certainly happened, but not on a large or well-documented scale and not in the vein of Xenophon's Ten Thousand or the White Company. In addition to mercenary work, I'm sure that many ronin joined up with the wako, a blanket term for multi-ethnic groups of pirates that raided the coasts of Japan, Korea, and China.
As far as specifically working for other polities around Asia: there wasn't any evidence of it that I knew of off the top of my head, but when poking around to shore up what I knew about the many small ethnically Japanese enclaves etablished as part of the intra-asian sea trade (more pre-sakoku edicts, though many did persist as part of the Red Seal trade), I did find a few references to this recent monograph. While it's focused on one particular man, it overall tells the story of one such enclave in Thailand, which the jacket summary/reviews imply involves a significant amount of helping out the Thai army for pay (before these actions eventually cause their ejection from the country). Might be worth a look.
The Sengoku period (1467-1573) is just a little too early for Japanese samurai to have been commonly serving abroad as mercenaries.
The first accounts of Japanese serving abroad as mercenaries come from the late 16th century. This practice mostly stopped in 1639,when the Tokugawa bakufu implemented Japan's closed country edict.
For a brief period, of some 40-50 years, however, Japanese mercenaries were abroad in Asia.
In 1603, Japanese mercenaries serving the Spanish were helping put down a Chinese rebellion against Spanish rule in Manila. In 1606, a company of Japanese mercenaries serving the Portuguese in Malacca helped defeat an attempt by Dutch Admiral Cornelis Matelief de Jonge to capture that port. In 1614, Englishmen of the East India company killed eight Japanese mercenaries in a skirmish at Ayuthia in Siam.
The largest employer of Japanese mercenaries may have been the kingdom of Siam. By the 1630s the Dutch head of the Factory in Ayuthia reported that the Siamese had 500-600 Japanese soldiers who were regarded as elite troops.
There is a report that as early as 1579, some 500 Japanese mercenaries were employed by the Siamese to help fight off an invasion by Burma.
Yamada Nagamasa was the most famous Samurai employed by the Siamese crown. He was married to a Siamese princess and given a province in Siam as a reward for services in putting down a rebellion in Siam. He was poisoned by rival Siamese in about 1630.
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