It should be safe to shoot
Those .38 S&W revolvers were essentially a Military & Police fitted with a .38 S&W cylinder. Most were 'converted' to .38 Special simply by, as Ram Slammer correctly mentioned, reaming out the front end of the chambers to allow a .38 Special cartridge to fully enter. However, because - as already mentioned - the S&W round is wider at the base, usually Special cases get bulged at the base. In extremis, they split.
However, the basic cylinder is pretty much identical to the same era .38 Special cylinder in terms of size, material and treatment. Unless the 'conversion' was seriously botched, the cylinder should be suitable for .38 Special regular loads. As Ram Slammer said, the chambers should still allow the wider S&W round to be loaded. However, as Woad Yurt pointed out, this conversion sometimes had the side effect of altering the cylinder to barrel alignment and fouling up the accuracy potential.
All those revolvers that were converted in such manner are 'ruined' as far as collectors are concerned.