If a Longtooth Shifter is in Wild Shape with appropriate fangs, and Shifts, can it use a bonus action to make an unarmed strike?
While shifted, you can use your elongated fangs to make an unarmed strike as a bonus action. (Wayfinder's Guide to Eberron, p66)
I think it should work:
You retain the benefit of any features from your class, race, or other source and can use them if the new form is physically capable of doing so (PHB p67)
The question is how strongly the attack is tied to your Shifter body.