Pyrodex or 777 will work just fine in your percussion pistol.
I'm reasonably sure your pistol is a smoothbore.
Bullets require rifling to spin them so they will remain stable after they leave the barrel. If they don't have this spin or it is too slow, elongated bullets will tumble but this might not be noticable at close ranges. Especially if they are shot out of a pistol that doesn't have sights on it.
I guess the real problem is trying to find a bullet that will fit in the barrel. As you may know, .45 caliber bullets for modern guns are larger than .450 in size. A lead Colt .45 bullet is .452 in diameter. Two thousandths of an inch doesn't seem like much but if you were designing something and you wanted a moderately heavy press fit on a diameter of .450 shaft, a .002 interference will produce a heavy press fit. Also keep in mind, lead bullets made for modern guns are usually made from hard lead, making it less likely that it will "give" when it is forced into a barrel.
Although the Cap & Ball pistols do use interference fits between the chambers in the cylinder and the ball/bullet, the extra material is sheared off of the projectile by use of the loading leaver which produces a LOT of force. Much more force than one could exert while loading a projectile into a muzzleloading barrel.