I think you will be able to do this. Just go on the first day and sign him and explain that he 'just' turned 13 and you want him to be with kids closer to his age (10-12).
We always travel on my twin DDs birthday, and the year they turn 13 I plan for them to still go to the lab (they will be 12 the day they board, turn 13 during the cruise). Last year I did this with no problem with the 8/9 group. My DDs turned 10 on the cruise, but I put them in the 8/9 group (I prefer for my kids to the the 'older' in the group rather than the 'youngest'.). They were fine!
I think it is easier to go 'down' than it is to go 'up' in age groups as long as it is within a few months of the cut off.
DJ