For EDC and quick and dirty cord work I carry a Black Ops Delta torch lighter. It is admittedly a little hot for paracord work, and one must be careful not to damage the work when melting ends to finish a piece. In general, a non-torch lighter is more controllable for cord work, but will take longer to seal an end.

My knot kit contains an old Zippo with a butane "flame" (as opposed to "torch") insert that works well for rough work.

When using a lighter I will whenever possible clamp the cord to be cut with a pair of locking "Forceps" (my surgical tech friend tells me they're not actually forceps but…), trim the line along the forcep edge, and apply the heat from the lighter. I usually take the time to trim the core short of the jacket, then trim and heat seal the jacket for the cleanest possible edge.

However, when precision is called for, a hot knife works better than a torch. I've found that most of the "cheap" hot butane hot knives don't really get hot enough for paracord (or take forever to heat up.) For portable use my pick is the Weller P2KC Professional Self-igniting Cordless Butane Soldering Iron Kit Quick & easy to light—it has a built-in ignition. Fast to heat. Burns just a little hotter when charged with ISOPRO stove fuel using a Primus Filling Adapter. (I charge all my Butane lighters with camp stove fuel canisters.)

For bench use in the shop, nothing beats the Engel Heat Cutter HSGM Hot Knife. A remnant of my work rigging racing yachts, and total overkill for paracord, but it is the ultimate tool for cutting line quickly and cleanly. That being said, I probably use the portable Weller 50 times as often as the Engel these days because I'm generally not knotting at my "big" workbench and for small diameter cord, it's just as fast and effective.