Usual reply: [I can assume NO responsibility for shooting an antique firearm, regardless of which powder is used!]
First, have the gun checked over by a gunsmith familiar with this type of gun! Pay attention to the condition of the barrel. Clean it first. Some of what appears to be pitting may actually be leading. If it is badly pitted, however, it may not be safe to shoot with any powder. Some minor pitting may be acceptable. Pay particular attention to the condition of the chamber. If it is badly pitted, it may cause extraction problems. Have the gun's headspace checked. If the 'smith doesn't have a set of headspace gages, it might be a good investment to buy some from Clymer or Brownells, especially if you plan to acquire other guns of the same caliber. IF the action closes on a NO-GO gage but NOT on a FIELD gage, it may be safe to shoot, but back you sizing die off until the action will close with just a little feel.
Slug the barrel to see what the groove diameter it has. .44 WCF Winchester barrels were supposed to have a nominal groove diameter of .427", but I've seen them all over the place, even as large as .434"! About the largest bullet readily available is .430. If the barrel is in that range, try making a dummy round with that bullet and see if it will chamber easily. Winchester .44-40 brass has the thinnest walls, but you don't want a cartridge so large that you have to force it in the chamber or you may raise pressures! If the groove diameter is so large that you can get bullet that size, you may need to use a very soft bullet, hollow base, and maybe have to stick with black powder to get the bullets to expand into the rifling. On the other hand, smaller barrels may work well with smokeless powder and hardcast bullets. STAY WITH LOADS IN THE RANGE SHOWN IN HANDLOADING MANUALS.
Good luck!