An AA FA was suspended for uploading pics from the employee rest area, and an AirAsia attendant was fired for letting her child in the area, so save putting any employees in an awkward position and don't even ask for that. The cake sounds safest.
I flew to Asia on four of my last five birthdays. Hitting the international date line and having it be my birthday actually makes my birthday shorter. Being on a plane also ensured there were to surprise parties, as my first year doing this was a milestone and there were threats of a party. Only once was the birthday even mentioned. A male FA came to my seat and quietly said "Happy Birthday." The GA noticed when looking at my passport and told the FA. I was Diamond at the time, so that may have been why.
On a DL flight to BKK, back when they had those, I was sitting across from a family with two young children. We landed a few minutes late. The pilot announced it was 12:15 am and the older girl, maybe 5, excitedly exclaimed, "Daddy, it's Ginger's birthday." lGinger was obviously the younger child. She started singing "Happy Birthday" and pretty soon everyone sitting nearby joined in.