Advice washing / cleaning 30s -40s non crepe rayon

It sounds like you're firm on the rayon part, and I believe you are saying it's a smooth weave, not crepe.

You can hand wash non-crepe rayon in cool water with detergent. You're right to remove shoulder pads for washing. In my experience, a good dry cleaner will make sure the padding doesn't wad up by pinning it in place, but for washing it's best to remove the pads. For washing you would also want to remove metal or covered buttons to prevent rusting. To check for the possibility of dye bleed, you need to test the fabric in an inconspicuous spot on the dress. Moisten this spot with a little of the detergent and cool water you'd use for washing, let it sit a moment, then dab with a white towel to see if the dye comes out. Embroidery and other details should also be checked this way.

In my experience, you certainly can dry clean rayon from the 1940s, but there is no guarantee that stains will come out. If you know what kind of stain you are working with, that helps.

 

Oh, I'm glad to see you've made progress on the stains!

Underarms are always hard. My best way is soaking a washable, sturdy-enough vintage item with an oxygen bleach product (Biz, dissolved Oxiclean, Etc.). Your dress may be too old for this working, and it may be a bit too delicate as well. If you are going to try this, definitely test for dye bleed with the product, and leave the test spot for awhile to see if it does any damage to the fabric. For me, this works best on cotton and on things newer than 1950 or so.