hi can anyone help me i am looking for the birth of william stuart ( ? surname)

dob 13/08/1898.

this is my grandfather on my dad side our name is mckinnon and i thought this was his birth name,although scotland bdm has no birth recorded on this date in this name leading us to believe he could be illegitmate.

he married my gran in southampton in 1938 whilst serving in the merchant navy my dad was born later that year,william left my gran in abt 1942 and

they had no contact after this date.

his date of birth and place of birth(falkirk) were found on his seamans cards which i got from southampton maritime dept.

on my grans marriage cert it has williams father as willam mckinnon(deseased) his occupation moulder.

whether this was his real father or step father i dont know.

i have know information on his mother.

any help would be greatfully recived.