The alien species that infects Wolverine in X-Men '97 season 2's fifth episode is the Brood.
The Brood are parasitic, insectoid extraterrestrials introduced in Marvel Comics by writer Chris Claremont and artist Dave Cockrum. They first appeared in Uncanny X-Men #155 in March 1982, where they served Deathbird, a Shi'ar noblewoman. Their horror comes from reproduction: they implant eggs into living hosts, and the resulting Brood can inherit the host's memories, appearance, and abilities.
The season 2 episode is titled “Weapon X, Lies, and DVDs.” It places Wolverine, Morph, Sabretooth, and Lady Deathstrike in a conflict involving Weapon X and the Brood. The species is sometimes confused with the Shi'ar, Skrulls, or Kree because all are major alien civilizations in X-Men stories, but those are distinct groups. The Brood are specifically the parasitic hive species associated with infection and transformation.
Wolverine's connection to the Brood also has a comics precedent: his healing factor once helped him purge a Brood embryo. That earlier storyline is one reason the species is such a natural threat for him.