would walnut veneer work as a backing? or Could edgebanding work as a backing instead?

I've never tried it but I wouldnt think it would be thick enough to carry much of the tension load. Maybe someone else will chime in that has tried it before.

No, Walnut isn't all that great for tension.  A 1/42nd veneer would not help at all.  

What is the bow made of.

If you want to back a bow with something that thin go to rawhide.

Its a hickory molly with a trapped back, I was more thinking of making it pretty with the veneer more than strength because hickory is already so strong...

but It was an idea for my next bow..

I know it sounds funny but a Hickory bow with a Black Walnut lamination core with a Hickory backing makes a great looking bow.