On OPR on Scotlands People, there "may be" a record for
William Stewart. It is dated 18 Feb 1759, but you can't tell if this is the baptism date or birth date until you open it for five credits.
Its bare details reads: 18 Feb 1759. William Stewart.
Parents John Stewart & Mary Stewart. Lismore Appin and Duror, Argyll (GRO 525/00 0010 0009)
And it might not be him, because having had a look at your public tree, I see that you have William's father's name as something else.(Forget what it is for the moment, but it isn't John)
Also, I enclose copy of a very brief note about a marriage in Ireland for William Stewart and Charity Freeman ML25 (See attachment)
I realize that you might already have seen the above information.