Cut it by slicing down through it onto a chopping board - it frays less that way than just looping it over the blade. Then just melt the end with a windmill lighter or blue flame torch, failing that, the gas ring. With wet fingers you can taper the end before it sets if you want to.
I find a blue flame torch is so precise I can tie a cord loop using a double fishermans knot, cut the ends as close to the knot as I can get, and melt them flush without damaging the knot or rest of the cord. Neat when you're doing lanyards and stuff.
BTW heat shrink tube is OK but it never lasts long, always pulls off unless you get the version that is adhesive lined as well.
Cheers