The Blue Book of Modern Black Powder Values shows several CVA pistols that it could be.
In addition to the Hawken shown above, they made a "Kentucky Pistol in .45 or .50 caliber (10 1/4 inch barrel), a Mountain Pistol in .45 or .50 caliber (9 inch barrel),Siber Pistol in .45 caliber (10 1/2 inch barrel) and a Tower Pistol in .45 caliber (9 inch barrel).
All of these except the Hawken Pistol are Percussion ignition guns. The Hawken was offered in both Flintlock and Percussion.
Mykeal's suggestions for a ball diameter and powder load could be used in any of them although I would go as low as 30 grains of powder in the .50 caliber gun making the load range 30-60 grains.
In the .45 I would suggest 20-45 grains of powder as a good range to work in.
If the gun is a Percussion style gun, the #11 percussion cap size should work without problems. The #10 caps may be too small and not fit the nipple properly.
As for powders, you will find that real black powder works best in any of these guns.
If the gun is a Percussion style, the synthetic powders like Pyrodex, 777 etc will work but you may have some mis-fires if you use them.
For loading pistols, I prefer a fairly loose ball/patch combination to ease loading so I would suggest a .010 or .012 thick patch.
The thicker .015-.018 patches will work in your gun without any danger however they may be difficult to start into the barrel and ram down to the powder charge.
zonie