I don't see why you couldn't do it, although I can probably give you a number of good reasons why you shouldn't.

I've seen more than a fair share of Internet FAIL videos where people break the bottle because they have no clue what they are doing.

Truth be told, most of the champagne I've ever opened, the cork comes out TOO easily. Hold the bottle upright and steady, (don't shake, unless you've just won the Tour de France), remove the wire protector if you haven't, and give the cork a slight twist (about 1/16 of a turn). Aim. Fire.

Of course any blunt or sharp force to the bottom of the overhanging cork will achieve the same purpose. It really doesn't take much at all. But my concern would be that the sgian has a very short blade and a) you might hurt yourself and b) it might look pretty goofy and awkward.