The Creature Can't Invoke in Animal Form
In the transition from Dungeons and Dragons, 3rd Edition to Dungeons and Dragons 3.5, many creatures--likely including the hengeyokai unless the DM rules otherwise--who previously used an ability like the spell polymorph self to assume different forms now use the supernatural ability alternate form.
While in an alternate form
The creature retains any spellcasting ability it had in its original form, although it must be able to speak intelligibly to cast spells with verbal components and it must have humanlike hands to cast spells with somatic components.
Emphasis mine. This likely includes warlock and dragonfire adept invocations unless the DM rules otherwise. I ascribe more weight to the creature's inability to employ somatic components than to the reason the creature employs somatic components; an alternate reading--like Mourdos's answer--does the opposite.
However, the only official changes made to the hengeyokai race in its update to Dungeons and Dragons 3.5 in the article "Oriental Adventures Update: Eastern Flavor" (Dragon #318 32-48) were changing the race's type to humanoid (shapechanger) from the type shapechanger and removing the hengeyokai's +1 Level Adjustment.