I'm not sure what you're expecting; the entire primary source material on ulfheðnar would easily fit on a business card. There are only two sources mentioning them. First, a passage in Vatnsdæla Saga saying:

... stórir höfðingjar ok þeir berserkir, er Ulfheðnar váru kallðir; þeir höfdu vargstakka fyrir brynjur (Finnur Jónsson's edition, 1934)

Meaning ... great cheftains and their berserkers, who were called Ulfheðnar; they wore wolf-pelts as mail

The second is in Grettis Saga Ásmundarsonar:

Þá hét konungr á berserki sina til framgongu; þeir váru kallaðir úlfheðnar, en á þá bitu engi járn; (Guðni Jónsson's edition, 1936)

Then the king called on his berserkers to advance, they were called úlfheðnar, and on them no iron would bite [i.e. have no effect]

All this says for certain is that it was a term in 13th century Iceland for a kind of legendary historic berserker.

We don't really know exactly what a berserker was either; and there's a lot of bad information out there, like that they'd eat mushrooms or more specially Fly Agaric, which is a theory that's from as far back as the 18th century, yet lives on despite being thoroughly debunked. A literal interpretation (as the term means 'bear-shirt') is that they wore bear-shirts, but a theory that's gained some proponents (e.g. Neil Price) is that they'd 'become' bears in a shamanistic sense before battle; although others have for instance pointed to the a literary account of a berserker having an seemingly normal conversation just before rushing into battle as an argument for them not having been in a trance (or high on mushrooms).

Berserker is more well-attested than Ulfheðnar though. The earliest possible mentions of it are as a name, a compound formed from the name Hiðinn/Heðinn (Old Danish Hithin, Old Swedish Hidhin, Old West Norse Heðinn). There's a number of names formed from Ulf- such as Ulfgæirr and Ulfhildr etc. (Peterson 2007)

The meaning and etymology of the name's suffix is uncertain, but it it not the same word as Old West Norse heðinn as in a fur garmet. It has been suggested that the West Norse form of the name Hiðinn became Heðinn by association with that word, while others consider the /i/ to /e/ change an expected one.

In any case it's as a name it occurs in the earliest sources, once during the actual Viking Age on the rune stone Sö 307; first word at the bottom left: ul(f)hiþin (damaged f rune missing a bistave), Runic Swedish Ulfhiðin. It's RAK style and roughly early 1000s. In an Icelandic context it first occurs as a name a few times in Íslendingabók from the 1100s.

Therefore, it should be at least a possibility that the concept of the Ulfheðinn was just a medieval invention through folk etymology: A name that'd by coincidence come to mean something like 'wolf-pelt shirt' in Old Icelandic was assumed to be related to Berserker (bear-shirt).

So the word as a term for 'wolf warriors' may not have been a thing in the Viking Age. On the other hand, shape-shifters were a thing in Norse folklore; Bödvar Bjarki who turned into a bear being most famous, but there's also an episode in Völsunga Saga where Sigmund and Sinfjotli steal magical wolf-pelts from shape-shifters who'd taken them off and gone to sleep and become wolves themselves, and complications ensue as they always do in folklore when you steal magical objects.

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Neil Price, The Viking Way: Magic and Mind in Late Iron Age Scandinavia, 2nd ed., Oxbow Books, 2019

Lena Peterson, Nordiskt Runnamnslexikon, 5th ed, Uppsala, 2007