captchee, with all due respect, "likelihood" is no more than an educated guess, based on theoretical circumstances.  it is not proof positive.  the only sole facts the op has to go by at this juncture would be historical records that reference his ancestry.  it's all amusing guess work.
. agreed but the simple fact is that we have non of that to go on . what we do have is predominance of a give  type and commonality of firearms during that time frame.
We also know that  while some folks are said to have shown up for militia duty  snap hence type  guns . I don’t recall but maybe 1 account of a fuse lock or wheel lock showing up .. But as you say , that doesn’t  preclude the  possibility of them owning one .
And yes its all guess work .  
  many many many things could have occurred 300 or so years ago.  firearms are important personal and family assets that could be from most any logical creator/location.  they could be had from anywhere, most any time prior or at the year/decade in question, and be or have been many decades old or "brandy new".  without at least anecdotal support records, it is all pure "i think" rather than "i know".  therefore, the op just needs to make a best guess, move on, and be happy.  as expected, ymmv, sir. 
 There is no given way to say “I know “ in this case .. I think I said that many times already . All we could do is go by the greatest probability . Which in no way completely removes the lesser probability .
 Yes guns are were and often still are passed down .  My uncle still owns  rifles  that my great ,great grandfather used to  fight the US Calvary . Hell,, as far as that goes  in the same old trunk were a couple  scalps from his father  .  My other uncle owns weapons used by  our family during the removals. I remember my grandfather showing me all of it as a boy .
 But that doesn’t mean that any of that was still used . Factually it wasn’t past being family  heirlooms and history .  Were the weapons still usable , well minus the bow ,  maybe .
 But then a quick turn  to my grandfathers gun cabinet, showed more modern  guns  a couple Winchesters and  Remington  rolling blocks . Later he owned a  bolt action.
 Today if I look at my own cabinet and compare what my father owned   there isn’t 1 American made rifle  or shotgun .  No muzzleloaders  and no BP cartridge, even though I  have both  and own both European and  US made .  Do I use his guns , well one of them  now and then .
 While this would seem to  prove your point , im not sure it factually does as if I were to have to chose  one of the guns  in the context  of what  the folks in this subject mater would have used them for  one might be very surprised at what I chose . But be assured it wouldn’t be one of the family heirlooms  .
So yes  the possibility is there that they could have owned most anything . But Imo there is a greater probability that  there would have been only a few that  would fit .
Still makes it a guess . No doubt about it   . but i think i said that more then once as well