The 38-40 is a misnomer because it is actually a 40 caliber, the bullets being only .025 less in diameter than the 44-40.
Now, 44-40's can be loaded down to some extremely mild recoil. I loaded a bunch of 44-40 cartridges with mild charges of very slowly burning rifle powder. The result was a recoil just above a 22 RF and less than a 38 S&W. I don't recall where I found the load published, but it worked very well to teach my daughter to reload and shoot a center fire. (Sometimes I thought I could just get a glimpse/see the bullet travel down range.) If shooting black powder, there is always cream of wheat and other fillers to "down" the charge. Even a wad and grease cookie will help fill the case and work to lessen the charge of black powder
