That will turn out so nice once it has been repaired.
I can't help with the tech info but if you don't get any informative replies here then here is the Art Deco Society website.
ART DECO & MODERNISM SOCIETY INC.
I'm sure someone there does restoration work and would be able to help.
It is unusual that the cabinet has veneer on it given the style.
Reapplying some veneer to those areas wouldn't be too hard but matching the stain or colour so it doesn't look " repaired " will be the trickiest part.
I'd hazzard a guess and say Queensland maple is the timber and probably shellac for the laquer.
Other more informed forumites may have a better idea though.
Stewie