Hide glue in N. America is usually casein glue. It’s pretty
similar and derived from milk I think.
For the iron-on Titebond method:
You want a PVA glue, preferably one rated for hot pressing.
Don’t fixate on brand names because they vary from country
to country. The cheaper consumer glues like Elmer’s in
N. America have cheap fillers in them. Elmer’s is fine for
joinery and I use it, but for hot pressing it crystallizes due
to fillers which would be a red flag in your application. Even
regular Titebond I is not rated for hot pressing and will
crystallize in hot press veneering but there is a version
of Titebond II rated for hot pressing.
Track down the data sheets for the various industrial PVA
glues available in your country and look for the ones rated
for hot pressing. Then try to find out if there is a version
sold to consumers in small containers.
In N. America the version of Franklin’s industrial hot press
PVA glue is “Titebond II Extend”, a white glue. The yellow
color of some PVA glues is dye and has nothing to do with
working characteristics from my research, just branding.
P.S. I agree with Paul M, the easy way to do it without
a vacu-forming hot press machine is with solid wood edging
shaped to the profile you want after gluing. You can
veneer the face of the panel before or after edging but
usually before is good.