Unfortunately, being asked to be the one who 'does the birthdays' in a workplace can often be a poisoned chalice, and the epitome of the phrase 'no good turn goes unpunished'.
At one place I worked, the staff birthday 'club' asked everybody who wanted to be in it to put in a fiver for each birthday, then they would effectively get back the equal value of all those fivers in one lump sum when it was their own birthday.
One year, somebody put in a fake fiver that looked fine at a glance but which was obviously fake when looking carefully at it for a few moments. I don't know if the contributor handed it over knowingly or not; but the kitty was obviously £5 short for the birthday recipient and nobody admitted it, so the man organising it - and who obviously didn't want to knowingly pass on a dodgy note or leave them inexplicably £5 short - saw no alternative but to put in an extra £5 of his own money.
Although it's a kind gesture of the employer to pay for it, it would actually be a lot simpler if it were funded by the staff themselves. That way, people are asked if they want to participate, they accept or decline, and everybody gets what they want.
Incidentally, does this man celebrate Christmas too? If not (as in he is actively against celebrating if he is a JW or something, rather than just of a different faith/mindset and sees it as irrelevant to him), this could be very difficult to navigate as well - although hopefully not your responsibility!