Can you provide a picture of the tuners...on the back side of the headstock? That might narrow it down a bit. From the look of the instrument in general, I would guess 40's/50's.
The oval Regal decal is from the postwar period, considered to be the 50's.
I doubt there are any '40's regal instruments, most of the Chicago instrument factories were doing war work then.
Your uke is most probably all Birch.
It's the same logo and really similar spray-painted rosette as my Regal parlor guitar, which I don't have a specific year on but am told is early 1950s.