Busy,
Either of those two would make a great Rabbit Gun, the Remington Pocket Pistol, or, the Remington New Army 44. I have BOTH of those pistols in my private collection. I have read however, in various reviews, that the pocket pistol is a bit underpowered at over 25 yards or so, that there have been statements made that at 25 yards, the pistol ball actually bounced off a fence post and did not penetrate deeply enough to lodge at all. I think thats because they propably used the reccomended "all round" load of 7 or 8 grains of BP, I load mine, with 12 grains, and I use slightly oversized conicals, not, round balls. I hand cast my conicals with a mold purchased directly from Lee Precision, a short 103 Gr 9mm pistol conical sized to .356 from the mold. (Dixie Mold #356-102-1R). I downsize the conicals in two steps, by first pressing them through a Lee .329 sizing die, and then, press them through a Lee .323 sizing die, which means they are just a slight smidgen above the diameter of the recomended .321 round ball diameter. The downsizing operation is a bit of a stress on both the dies and the arm, so, I lube up the bullets, tip to base, with cheap ol crisco vegitable grease, I would recommend this to you if you try this little trick of downsizing a standard modern conical bullet down to an appropriate size for BP use.) They are a bit tight going down, but I press them down into the cylinders using a loading press, I don't use the loading lever on the pistol, which is rather small and has a reputation of pulling through the pivot screw hole in the base of the loading lever, a known problem with these pocket pistols. I only use the loading lever to retain and lock the cylinder pin in place, and I carry spare cylinders and a hand held loading press with me in my possibles bag. The conicals seem to work just fine for me, although a bit of a bother to prepare and load.
I don't need to go to all that kind of fuss and bother with the 44 Cal however, as there are stock 44 caliber BP pistol conical molds of the correct sizing for the 44 BP Revolvers. The recomended load of 20Gr seems a bit light to me, I would go up a bit from there, to 25 or so. The cylinder of the 1858 Remington Army 44 Cal is a bit long, I can load it with a 35Gr charge, and often do. But I would think twice about using a 35Gr load on a delicate lil rabbit, might not be alot left !!! LOL !!!
The reccommendation from Charles (Above) about opting out for a shotgun is a good one, I know your preferance for home-builts and pistols, so my recommendation to you would be a .69 Caliber smooth bore pistol kit of some type loaded with a shot load. I had one of those, a flintlock kit pistol, back when I was your age, and I just loved the thing to death, I bagged many a rabbit with it back in the day, many times comming home with a brace of 4 or 6 rabbits in one afternoons outing. Great and FUN gun that !! The following pic is from the online Dixie Catalog, and it's a 50 Cal, not a 69 Cal, perhaps a bit over budget at $315.00 for the kit, but a very nice pistol kit at any rate.
Dixie also has a percussion 50 cal kentucky pistol, already assembled, not a kit, at $198.75, which is probably closer to the mark of where your budget may be.
Have fun with it !!!
Sincerely,
ElvinWarrior... aka... Dave, "EW"