The downside to loading 9mm bullets in .38 Spl cases is that most 9mm bullets are not designed with crimping grooves.
Also, that 0.001" difference in diameter does not seem like much, but it can be enough to prevent you from getting a tight bullet-to-case assembly. You probably have to use a .355" expander plug from a 9mm die set to get good bullet fit. I once loaded a couple hundred 9mm 125 grain RNL bullets in .38 Special brass. Most fired normally, but there was a wide variation in report, recoil, and accuracy. A couple bullets migrated out of the cylinder to jam the revolver, and I also got a couple bullet-in-bore malfunctions. In summary, it might be an interesting experiment, but the hassle (and hazards) of doing this outweigh the advantages (if any).