Never seen a flint J & S Hawken... rifle or pistol. Never seen a full stock Hawken pistol. So anything you do will be speculation. I suggest a half stock flint pistol. There are plenty of photos of flint half stock English style dueling pistols. They were very popular in America. In the book "Firearms of the American West" there are 3 examples by Philip Creamer... another St Louis maker that came from Maryland. There are several books on Maryland makers that have photos of half stock flint pistols.
There is or was a fullstock rifle in the Smithsonian Institute that was supposedly identified as a flintlock
Hawken rifle but whether or not that was ever completely established as FACT I don't know.
The rifles that were and are being offered as flintlock Hawkens are as you said,a speculation and there
are some good looking fullstocks with Hawken butt plates and trigger guard seen frequently.
I made a number of Ketland locks for these for a long time and used the last one on a personal project
in 2008. English half stock flintlock rifles are a favorite of mine and I had a brief experience with one owned by
the late Tom Dawson.It was a Manton and if there was any lag in ignition I could not here it .
Bob Roller