The veneer has been successfully applied to the top and front accent blocks of this radio.
For the top, the original I steamed off appeared to be black walnut. Once off, the top panel was just 1/4", panels of two species joined. I decided to add a second, whole panel for a substrate for the new walnut veneer to bond to. It can later be edge rounded using the router to mirror the quarter-round below it, a common art-deco feature.
Since the veneer "blocks" appeared to be burl maple, I chose the same species but it was thin and sort of lumpy.
I took advice of Bob Anderson and coated both veneer and base then letting sit for a few hours.
Ideally, I suppose the glue needs time to soak into both veneer and base substrate.
I used Titebond woodworkers glue spread with a foam brush, a thin but complete coating is enough. I clamped it a few hours later after the glue dried
Using my steam iron to remove old veneer was one easy task.
I used it again a day after to flatten any "bubbles" by re-softening the glue.
The veneer will need to be trimmed with a hobby knife for an original-looking fit.
The stain for the new veneer work has to be selected...but its hard to match the original colors.
The question is: do I match what the present finish is, or try to restore to the original color?

Here is the burl chip in the middle of all the stain samples I could use, after I hit the adjacent finish with Howards Restor-a-finish, the color may be different.

Many factors seem to affect the color you're trying to restore to after 77 years.
The patina of the wood, a characteristic of age, combines with an aging original finish to make something that is not exactly an exact match to a standard palette.
The remainder of this radios finish is faded and scratched and will be addressed also.