First of all, don't do anything until you have a satisfactory answer. The 'press-out' or 'seepage' from some glues can definitely mess up your finish!!!
That being said, don't think I'd use super glue. If I remember correctly, that's one of the problem glues (for this particular purpose; works great in other areas of repair).
I'll call my luthier and get a better answer for you. May take a couple of days, but I'll have something for you. If I'm wrong about super glue being on the bad list (it's possible, I turned 57 last Friday!), I'll let you know.
Again, don't do anything until you are sure you have the right glue for the job!