They don't even know what year, let alone what month or day. 12/25 was picked to coincide with prior pagan celebration dates, so as to diffuse/replace the pagan practice.

Hell, there's pretty much no record of Jesus's childhood...he's born with fan fare and wise men with gifts and stars shining brightly yadda yadda yadda, and then - apparently the next morning, the gifts are gone, the wise man are gone, and no one pays any mind to the lad, until he becomes an adult...when, BAM, he is The Saviour, yadda yadda yadda....

So don't worry about his birthday, if any one would understand you missing it, you'd think it would be Jesus for Christs Sake.