Is wood glue the best solution for real walnut (curved) veneer?
A good wood glue that I use is Titebond, types 2 & 3 are waterproof. Don’t use Gorilla glue or similar glues that expand when they cure. The biggest challenge for you depending on the curvature of your piece, will be applying even pressure on the veneer, without denting it since it is so thin. I don’t know how many repairs you need to make, one thng you might try is cutting to shape, a form out of styrofoam. Back it with a piece of wood, and cover the exposed (veneer side) styro with packaging tape (glue won’t stick to it, glue will stick to stryo though) and try clamping it up that way. I use a vacuum press at work for curved pieces, or I make a form for clamping curved pieces. If you don’t want to spend the money to have a professional fix it, or if you don’t have tools to make forms, you might try that styro form. The denser the styro the better. You will just need a clamp and glue. And try to use a thin, even layer of glue, you don’t want a bunch oozing out everywhere in your case.
