The 9 mm is nominally cast at 0.356" while the .38 will nominally be 0.358". That doesn't seem like much, but with lead bullets even the smallest gas leak can spray lead onto the barrel. Also the bullets tend to unbalance because they tend to bear against one side of the bore so the rifling cuts 0.002" shallower on one side. A friend of mine had an improperly manufactured .38 barrel that had rifling lands 0.006" tall on one side and 0.002" tall on the other. All bullets he tried were unstable and tumbled and keyholed and threw turkey platter size groups at 50 feet. I realize that's twice the difference you are talking about, but I wouldn't expect you to get good results based on the principle.
The only remedies I am aware of if you have to use such small bullets, are to, 1.) buy them soft, like swaged bullets, and fire them with a very fast powder, like Clays or N310, that will bump them up to full diameter with the sudden pressure impulse; 2.) squash the bullets slightly shorter and fatter in a press, then run them through one of the inexpensive Lee bullet sizing dies for .38/.357 on your loading press, though this won't provide great consistency but will eliminate some of the worst trouble. If by some miracle the bullets don't tumble badly from uneven rifling engraving, then you might prevent the worst of the leading by cutting base wads for them from low density polyethylene (LDPE) sheets. That will act as a gas check.
Sorry the news isn't better.