A heat gun to soften the silicone and a long retractable razor knife like an Olfa or something thin and flexible.
A thinner knife is better because it'll let you get better access. You'll probably break lots of blades so buy extras but I'd say this is going to be the best, safest way to get the overflow off. Once you have it cut back a little bit you may be able to slide some fishing line in behind and slowly saw it through the silicone, braided line works pretty well for this if you can find it.
Just please go SLOWLY and take your time, this isn't going to be a 5 minute procedure.