OK, this may be one of the most common things one has to learn about taking barrel pins or any small pin out of guns. You DON'T want just one punch, but you HAVE to have two punches. Both have to be right at or preferably slightly smaller diameter than the pin. One is the full length punch needed to drive the pin all or most of the way out. The second one has a SHORT length of the size punch you need and is commonly known as a "starter punch." A starter punch is REALLY needed when the pins were filed flush with the stock and are curved on the ends.
The Starter Punch is the key to get the pin moving. With the length of the pin punch very short to no more than 1/4" or 3/8" at most, the pin section will not bend/flex/break and will allow more force to break the initial mechanical bond when you first begin to drive the pin out. (After you get the pin moving, you use the longer length punch.) You can make an excellent starting punch out of an old Nail Set that is the correct size for the pin you want to drive out. Also, you can take a full length pin punch and cut it short by using a Dremel Cut Off Disc. Make sure the outer edge of the punch is slightly rounded or chamfered, so you don't have a sharp edge.
MANY muzzleloading, both original and repro, had their barrel pins filed flush with the curved surface of the fore end. This did not matter because most people never took/take the barrels out of the stock and the pins filed flush were "esthetically pleasing." If you run into this, you sometimes have to go to an even smaller starter punch to get the pin moving and so the punch doesn't skip off the pin and mar/damage the wood around it. Fortunately some builders today are using slightly shorter pins that are square and perpendicular to the body of the pin to make it MUCH easier to start the pin moving. There will be a little curved open space over the pin holes and that can be filled in with beeswax or one of those coloured crayon type wood filler sticks.
BTW, I ran into those curved ended pins on EVERY Brown Bess I worked on. I deliberately shortened the pins a tiny bit so the ends were square/perpendicular to the length of the pin, then filled the open space with beeswax JUST as so many original gunsmiths did. That makes it easier for the NEXT guy to get the barrel pins out, even if I never took the barrel out of the gun again.
Dry firing a flint lock with a wood flint 5 to 10 times a day will not hurt the lock at all, but it WILL make you a better shot!
Gus