That's scary. Since there's no box, there's no need to remove the insulation. Since there's no need to remove the insulation, but there is no insulation, it means that there probably is absolutely no insulation/sound proofing in that wall!
Anyway, the best you can do is seal the wall plate with something like this.
And if you're considering putting up another layer of drywall, then why not remove the current layer of drywall to be able to put sound proofing material in the cavity? The effort would be almost the same, but with better results.
Try to talk to your neighbor, see if they like the idea of sound proofing (And split the cost).