There is a bunch of history for the 44-40 WCF cartridge, originally known as the 44/100, then the 44 Winchester cartridge.
Originally a black powder cartridge for rifles (Winchester 1873, etc.) that then got chambered in the Colt revolvers, and most importantly to me, in the Remington 1875 revolver - go S/N 47!
See https://sites.google.com/view/44winchester for a bunch of info, and a link under handloading to BP-only loads (for rifles, sigh).
So, in my Lyman blockpowder reloading book are data for the 44-40 as a revolver cartrideg using black powder, modern primers, and cast bullets.
Also, I have a bullet mold for casting 0.427" bullets, I think. Lyman 042798 mold - web search shows this is a 205 gr 0.427" bullet for the 44-40 revolver or rifle loads. So, need to get some correct lead for the mold, and then cast a bunch of bullets. Also, need Pyrodex or other black powder. Looked up smokeless loads for the 44-40, and they are like 5 gr! In a case the size of 44 Mag! I am not a big fan of that. I think we do black powder and the cast bullets for the test loads for the Great-Granpa's shooting iron.
Lead-free bismuth allow for casting bullets - artfulbullet thread. This could be useful for the 44-40, but it looks like I should probably start with standard hardball or linotype, and go from there.
Get the metal from rotometals.com - they sell hardball (apparently equivalent to Lyman #2 alloy) for general handgun and some rifle cast bullets. About $20+shipping for 5 lbs. So, fairly cheap.
A web page with some info on powders, bullet casting, and bullet swaging after casting: Ballistic Assistant.