The scissors used are medical snips, available from a dive shop for quite a lot of money or a pharmacy for just a dollar or two.
When diving here I usually carry a small folding knife in a pocket, though occasionally I forget it. In my eight years of diving here I have never needed to use a knife underwater. I can't visualise a time when a snorkeller might need one.
When diving in cold water I always carry two knives, but again small folding ones. The old idea of strapping a large knife to your calf is passé, both because of the macho image and because the knife itself becomes a hazard and a prime cause of entanglement. And also because it's completely the wrong place to carry a knife.
IMO Harriette is completely right in advocating extreme care when using a knife. You should never cut anything you cannot easily see and feel. If necessary, take off your gear to inspect and access it more effectively.
In my entire diving career (thousands of dives) I have used a knife to help disentangle myself on just ONE occasion, and that was to cut away monofilament fishing line on a deep wreck.
If you're concerned about carrying safety equipment, take a bright orange safety sausage, a small flashlight, a mirror, and an extra-loud whistle. Forget the knife. And tell (responsible) people where you're going and when you expect to get back.