From the SASS shooters handbook ‘Sights may be altered to allow the gun to shoot to the point of aim, so long as the resulting sight appears to be “period”.’
As Del said many of the cap and ball conversions used dovetailed front sights. Dovetailing has be used for mounting the front sight as far back as handguns. Most of the flintlock pistols that I have seen have the front and the rear done this way.
The front sights that we are used to seeing are very difficult to set in to place, with out tooling meant for the job. They are slightly over sized and then pressed in to the barrel, the barrel then has to be crimped to the sight. This tells me that if you needed one replaced in the 1800’s by other than the most skilled gunsmith, a dovetail would be the best way. In modern times as well as the past after sight is fitted to the barrel it will need to be staked in place. After the windage has been adjusted a small center punch is used to push a bit of the barrel down on to the sight base preventing it from moving under recoil.