1930s roof with no felt lining, solutions without removing roof
Wood shingle roofs in Dallas used to be nailed onto strapping (battens) without any roofing felt underneath. Then when those shingles were worn out a layer of asphalt shinges was put over that, and I don't think roofing felt was used. (I do remember heavy wood shake roofs in the 1970s were installed with felt interleaved with the courses.)

If you have a 1930s roof and the wood structure underneath is not rotted, then you should leave it alone. When the roof needs to be be replaced, then probably OSB or plywood decking will be put down, and modern water barrier on top of that.