The difference in bullet diameter is so small that many S&W revolvers chambered in 38 S&W (well, .380 Enfield) for the British in WWII were modified after the war to take 38 Special. A hollow base lead bullet would be a very good choice. But:
1) Most good quality 38 S&W revolvers will have chamber steps to prevent the use of cartridges whose case is significantly longer than 38 S&W.
2) This may not be a good idea because of the possible difference in peak firing chamber pressure of a 38 Special wadcutter load compared to that of 38 S&W. The 38 Special wadcutter load was actually designed to duplicate the ballistics of 38 S&W, which had a very good reputation as a target load. But if the case capacity of 38 Special brass after seating the bullet to the correct depth is significantly different, than the pressure the load develops could be different, even if the muzzle velocity is the same. I don't have any reference books here, but you need to check on this before proceeding.
38 Special wadcutter is a light load, but many 38 S&W revolvers were kind of flimsy. What type of gun are you proposing to try this in? A solid frame Colt or S&W, or a top-break Webley or Enfield could probably take it, but would be very likely to have the chamber steps I mentioned first. A cheap top-break may not have the steps, but would be a much weaker gun. Of course, it could still be an interesting project.
I think that if this sort of thing was easy or convenient, a lot more people would do it, because 38 Special ammunition has been cheaper and easier to find than 38 S&W ammo for several decades.
