Your straight-wheelweight bullets should work just fine as they are, that is, without further hardening.
I'm shooting four .357s, an 8.375" M57 .41 Magnum, and several .44 Mags, all with aircooled wheelweight alloy and no leading problems. The most important factor is the fit of the bullet in the throats of the CHAMBERS, NOT the barrel! The bullets should not drop through the chambers and out the front of the cylinder, but rather should need a bit of a push to force them through.
My standard .41 magnum load uses the RCBS 41-210 semi-wadcutter, which drops at 217 grains in my wheelweight alloy. This is a plain-base design (no gascheck) and causes no leading whatever when sized at .4105". I'll maybe get a slightly larger sizing die some day, a .411 or .412, but in honesty, this bullet is already extremely accurate with 17.5 grains of 2400 doing the pushing. From that long barrel, the velocity is just over 1300 fps....NICE load.
Try your WW metal just as it is, first. That's a fine cartridge and it's easily loaded with cast bullets. Nice gun, too!