They have to dry for at least 60 days before they can be officially scored. I don't know how fast your taxidermist is, but if it's gonna be a few months before he can get to it, there's no reason why you can't keep the antlers with you till he needs them.
Back when I was doing taxidermy part time, I had some customers keep their racks with them for a while, especially the bigger ones.
It's nice to have them to look at and show friends.
Also, if you think it will be borderline on making 125", you should have it scored as soon as the 60 days are up. They will continue to shrink long after 60 days.