One of the biggest obstacles to using any conical bullet in a cap and ball revolver -- perhaps the biggest obstacle -- is the need to start the bullet straight into the chamber.
With balls this is not a problem, they're self-centering. Conical bullets almost always require a sub-diameter base or heel that slips easily and partly into the chamber mouth, to ensure a straight start on the bullet. The remainder of the bullet is larger diameter, so that when it's rammed it not only seals off the chamber from multiple ignition, but clings tightly to the walls of the chamber so it doesn't move during the recoil caused by other chambers being fired.
Unless designed specifically for cap and ball sixguns, most bullets are straight-sided. Trying to get the bullet perfectly aligned, in axis with the chamber, and then ramming it straight is nearly impossible. As soon as the rammer applies a little force to the bullet's nose, the bullet wants to tip over to the side.
Various physical laws, as well more than a few supernatural ones involving gremlins, the whims of the gods, and ancient family curses seem to work against seating the unheeled bullet straight.
If the bullet is not seated in line with the chamber, but is cocked to one side or the other, it will travel down the bore out of axis with the bore. Or, as they say in the Pacific Northwest -- kerslonchwise.
A bullet is like a toy top. Spin is quick and true, and it will run straight for a short time. Start that same top crooked and its orbit will degrade immediately and soon it will flop over and roll. A bullet that does not rotate in line with its axis will not be accurate.
It is difficult enough, at times, to get a properly designed conical bullet seated straight into the chamber, let alone one that wants to fight you every step of the way.
As noted above, the bullet must also be a tight fit in the chamber to keep it from shifting forward from recoil. In black powder firearms, a dangerous condition exists if there is a space between the projectile or wad, and black powder. This space can create catastrophic pressures.
So, a bullet that is little more than a slip-fit into a cap and ball revolver's chamber -- even with grease over it to discourage multiple ignition -- can cause major problems.
Don't waste good, modern bullets in a cap and ball revolver. Save them for the caliber for which they are intended.
Incidentally, every once in a while someone asks how to load jacketed hollowpoint bullets in their cap and ball revolver. I advise against it. You can bend the rammer lever and its parts trying to get a copper jacketed or plated bullet started.
The 8th edition of Handloader's Digest (1978) has quite an article by John Lachuk on using jacketed bullets in cap and ball revolvers (p. 46). He used a Ruger Old Army and replicas of the Remington Army and Colt Walker. He had to ream out the chambers of his revolvers to .451 inch, then adapt a MEC shotgun shell resizing tool to use as a rammer.
Frankly I feel the whole experiment, while interesting, was more trouble than it was worth. Jacketed bullets create greater pressure than lead bullets, because of their greatly increased friction. Lachuk also used a small priming charge of a fast-burning smokeless powder under the black powder -- a practice long known to not only increase pressures but to blow up guns!
Cap and ball revolvers, regardless of their vintage or design (are you listening, Ruger Old Army owners?) are NOT designed for smokeless powder. Period.
It's a wonder that Lachuk didn't blow up a gun or two. The gods were kind; they can just as often be malicious.
Returning to your original question -- save yourself frustration and use conical bullets designed for cap and ball revolvers. Better yet, use the humble ball. You'll almost certainly find the ball more accurate, much cheaper and easier to obtain.
For the .44 caliber, use balls of .454 or .457 inch. The Ruger Old Army is something of an exception, requiring balls of .457 inch. For the .36 caliber, use balls of .378 or .380 inch.
The increased diameter ball, when rammed into the chamber, creates a wider driving band for the rifling to grip, often enhancing accuracy.
Save those .45-caliber bullets for the day you get a .45 Colt, or trade them for proper conical bullets for the .44 cap and ball sixgun.