I used to use 4F and then got tired of having to have two granulations. You should be just fine using whatever you use in the bore for under the flint.
Military flintlock muskets utilized hand made cartridges - F & I, Rev War, etc. If you study the drills for loading, you'll see that the tail of the cartridge was torn open and the musket was primed FIRST utilizing the same powder that then went down the bore.
I have a fusil de chase - .62 (20 gauge). Normally, I use 2F in it but I have gotten caught short and used 3F. Both granulations worked well for priming. I don't have my long rifle any more but that was a .36 with a large Siler - the 3F worked just fine with that one.
I do however, carry my priming powder in a small horn. My large horn is quite large in the F & I War era style and I really don't want to prime the pan out of it.
When I first started shooting flinters, I made a priming container out of a section of large deer antler and put one of the brass push priming spouts on it. It worked well with the 4F but I just didn't like it - I like a more traditional way of priming.
If your lock is tuned and your flint adjusted to give a good shower of sparks - a coarser granulation shouldn't be a problem.
If a pair of '51 Navies were good enough for Billy Hickok, then a single Navy on my right hip is good enough for me . . . besides . . . I'm probably only half as good as he was anyways. Hiram's Rangers Badge #63