ND: I get what you're saying, but I don't agree in this case. Shifter is the "half were" race, and is tied to lycanthropy, bloodlust, the moon, therianthropic regeneration, being a predator, and so on. Hengyokai is the "faerie animal that turns human" race, and is tied to the fey, to specific traits based on animal, spirit stuff, trickster stuff, and so on.
Frankly, aside from the animal part, they just don't have much in common. I wouldn't want to use a shifter template for the wolf from
Ivan and the Firebird; that's a magical shapeshifting animal. Nor would I want to use a magical animal race for someone with loup-garou blood in them. The myths are simply very different.
Mechanically, I'm just not seeing any overlap; any reason to combine the races, I mean, there are 36 shifter feats. 8 of them are longtooth, 9 of them are razorclaw, 11 are both. So lets look at the remaining ones:
Sturdy Shifter: would be broken with Hengayokai. (gain 5/10/20 temps whenever you use your racial power).
Crow's Flight: ignore difficult terrain when you run, +2 to athletics and acrobatics. Ok, this one would likely be ok.
Blood Devourer Shifting: All about therianthropy and bloodlust. No.
Draw out the beast: Treat yourself as bloodied. Intended to synergize with the shifter bloodlust abilities.
Shifter's Agility: +5 to agility/acrobatics when you use your racial power. Actually, probably ok, though strong for a skill feat.
Wild Senses: +3 to initiative, bonuses to track. Probably ok, though not really appropriate for all Hengayoki.
Holy Savagery: All about being bloodied. No.
Urban Predator: More predator stuff, but not awful.
So, they'd gain what? 4 feats for making them shifters? Plus access to 4 more feats that aren't appropriate, one of which is broken?
Fundamentally, your principle isn't bad, but you're wrong here. The two races have no conceptual overlap.
Henkyokai is about being part animal. (and about being fey, something completely uncovered here).
Shifter is about being part -monster-.