For a pistol, I would use a brad point drill. Even though the barrel is only 13" long, you will only be drilling about 5" worth of wood. I would buy the right diameter drill, probably 5/16", I should remember since I did all the barrel inlets and drilled the ramrods for the class guns. My personal pistol drill is a 5/16" brad point bit with a 1/4" shank. I took a piece of 5/16" drill rod and bored a 1/4" hole in the end and then silver soldered the bit to the extension. Drilling a pistol is no big deal. The main thing you need to do is make sure the groove is pointed to where you want the drill to end up and clear chips often.
If you want something exciting to drill drill the ramrod hole for a blunderbuss. I just inlet 9 barrels in Turkish walnut for Ron's upcoming class at Bowling Green. The ramrod groove is actually curved the first 9" to follow the flare of the barrel and then straightens out for the remaining distance. I just mad a setup and drilled the first one yesterday. Came out dead on. Hopefully I can drill the other 8 to match. Had to make myself a special "flex" drill. Good thing it worked as I drilled the first one on an actual student stock.
Dave