The M57 cylinder will be too large in dia both in the throats for the 38-40 bullet and in the forward 41Mag chamber area for the 38-40 cartridge chamber .
The 41Magnum is a straight case at .434 base to mouth.
The 38-40 is larger in dia than the 41Mag at the base which will clean up the 41Mag chamber OK.
But the neck of the 38-40 is only about .417/.418 depending on who you check for specs. The brass is very thin on this case.
The 41Mag chamber is already too large in dia at this point.
The .41 Magnum cylinder throat @ .410+ is way to large already for the 38-40 bullet.
A 357 cylinder will work.
Even the orig 38-44 revolver is a good candidate if the OAL of your loaded 38-40 ammo fits the OAL of the 38-40 cylinder that's on the gun now.
The 38-44HD has been converted to 38-40WCF.
Rebore or Reline or Sleeve the HD bbl to 38-40 and have the cylinder rechambered to 38-40 w/o recessed rims and you are there.
You will likely have to make a new front site blade pinned into place for the different elevation needs.,,but maybe not.