[Arran]

I am not an expert, but that looks like mahogany, AKA luan plywood.

No, It's not Luan plywood, it's one of the mahogany look a likes, sapele. or possibly quartersawn makore. G.E listed what sort of veneers they used in their advertising and I think that they liked to use one of those veneers, particularly of the ribbon striped variety, on their cabinets in the 1938 and 39 model years.
 
http://www.wood-database.com/lumber-iden...ds/makore/

http://www.wood-database.com/lumber-iden...ds/sapele/

Regards
Arran

That Makore looks like a possibility.

 Better strip some of the original finish off, just to make sure, G.E was like many manufacturers in that their cabinets had a tinted finish over everything to even out the variations in wood grain.
Regards
Arran