Short answer:

The swords carried by the Japanese during WW2 were typically mass produced, not associated with "the samurai", of ordinary quality, and analogous to the "Luger or helmet" you mention.

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Discussion

It would be very unusual to find an historically important sword worn by a Japanese soldier on the battlefield during the Second World War, so the question has a mistaken assumption. Museums may display these for their association to the War, but they're not typically any rarer than a grenade or rifle, a routine bit of military kit of no particular value.

Technically, the era of the "samurai sword" ends with the Meiji Restoration and the abolition of the traditional rights of the samurai to wear swords in public (and to cut down commoners). From this point on, swords were worn by the uniformed military, but no longer marked the distinctive martial class as before.

If there were a particular "samurai sword" of note which had been taken as a trophy, decency and the law would require that it be returned-- but I can't find an example of anything like that. Historically significant katana to come into US possession would almost certainly not have been worn in battle or taken as trophies, but rather acquired during the Occupation.

What swords did Japanese wear? Typically mass produced weapons of ordinary quality and no historical importance, and as the war progressed and Japan's situation became more dire, the quality got worse. A few officers might have worn a sword that dated back some time, but that was the exception, not the rule-- and I can't find an example of such a sword being taken as a trophy, though it could have happened.

The "Gunto" [ 軍刀 ] meaning "military sword" was adopted after the Meiji Restoration; those used during the Second World War were largely produced at the Toyokawa Naval Arsenal and the Seki Arsenal. The most commonly encountered example is the "Type 98 Shin-Gunto" (= "new military sword"), and these are still found in tremendous numbers, a good example will be worth a few hundred to perhaps a few thousand dollars. These are distinct from "日本刀="Nihontō= "Japanese sword", which do have historic value, but which were not mass produced for military use.

To the extent that they have any value beyond souvenirs/military collectibles, it would come from a distinguished prior owner, if known. But in general these items are not particularly valued by the Japanese, nor by collectors-- they're a novelty, like binoculars or maps. Ironically, its essentially illegal for an American -- or a Japanese -- to have a guntō in Japan; because they have no historic value, they are classified as prohibited weapons.

There are items which _do_ have an emotional resonance for Japanese families, but they are not these mass produced swords. A far more important item, one which families will typically want and where returns are organized are the distinctive sashes made by folks at home -- "Senninbari" (千人針 = "Thousand man stitches"), a strip of cloth with propitious stitching, made for a soldier departing Japan by his wife/mother/sister.

At the Showa-kan (昭和館 = "Showa Hall", with "Showa" being the reign name of Emperor Hirohito) you'll find a display of senninbari and letters home-- these are the memorabilia that matter to the Japanese. The guntō have no particular importance, being less personal.

Much more troubling are more intimate trophies taken by soldiers-- notably skulls. It is an upsetting and unfortunately still necessary call to specialized forensic anthropologists to identify such items as turn up from time to time

A small subfield of forensic anthropology concerns the identification and analysis of human skulls collected by military personnel as war souvenirs and trophies. Most of these relics originate in two twentieth-century conflicts: the Pacific War and the Vietnam War.' Many have come to light quite accidentally. In June 2003, for instance, detectives in the city of Pueblo, Colorado, searching a house for drugs, discovered a small trunk inscribed with the word 'Guadalcanal' and the date 'November 11 1942'. Finding a human skull inside, they seized it. Photographs taken by the coroner's office, and published in a local newspaper, showed that the skull bore many inscriptions . . .

The skull also bore autographs of two or three dozen servicemen up to the rank of lieutenant colonel, and had been lacquered. The householder told the police that it was a family heirloom, and demanded its return. It was the skull, he said, of a Japanese soldier killed in the battle of Guadalcanal by his great-grandfather, Julius Papas. Papas and other members of his unit had signed their names and ranks on it and given it the nickname 'Oscar'. Forensic analysis by anthropologists at the US Army Central Identification Laboratory confirmed the probability of wartime Japanese origins, and in May 2004 the skull was handed over to the Japanese authorities for interment.

If it's not too nauseating, letters from soldiers explained fairly frankly what trophy hunting was like

We looked all over the island and in the hospital cave where the last fighting took place. There were dead Japs all over the place and I thought of sending Pack his Jap skull, but most were still being used slightly. We got some pens and stuff out of the pockets and one of the fellows got 2 bayonets. I got a rifle and other papers. There were a lot of helmets, canteens etc. lying around. The Japs were pretty ripe and one of the boys got sick

So while there's a mystique of the "samurai sword" -- that's not what those souvenirs of the Pacific War are; they are very ordinary guntō, not nihontō or a weapon that might have been wielded by Musashi Miyamoto or Date Masamune. There are, however, other kinds of souvenirs which are both immoral and illegal to keep, which do turn up from time, and which are returned to Japanese authorities through proper channels.

Japanese remain sensitive to human remains that have not been repatriated-- very recently a Japanese delegation requested the return of the remains from the Aleutian Islands, where some thousands were buried in mass graves.

[T]he grandson of a Japanese colonel who died in that fight spoke out. Nobuyuki Yamazaki called for the remains of the Japanese soldiers who died on Attu to be returned to their homeland.  

“There are still 2,319 remains of Japanese soldiers on Attu. During the war, the U.S. Army buried the Japanese soldiers’ bodies with care, built a memorial, set up a grave post and paid respects to the spirits,” Yamazaki said, as he read from a prepared statement in Japanese, which was translated into English for the audience.

“We war-bereaved families wish to take all the remains back to our homeland. We have requested this through our Japanese government three times – and 3,948 signatures have been collected,” Yamazaki said. “Japanese people find great comfort when the remains of the Japanese are buried in our homeland.”

References

The Decline of the Japanese Warrior Class, 1840-1880

The Progress of Japan and the Samurai Class, 1868-1882

The Shôwa Hall: Memorializing Japan's War at Home

Trophies of War: U.S. Troops and the Mutilation of Japanese War Dead, 1941-1945

Skull Trophies of the Pacific War: Transgressive Objects of Remembrance

How Do You Bring a Sword In and Out of Japan? All About Japanese Sword Laws

The Connoisseur's Book of Japanese Swords

Japanese families request remains from Battle of Attu