As long as you and your son are only making guitar/microphone cables occasionally, a repurposed hair drier typically works fine, can usually be rounded up for free, and is unlikely to damage anything. I'd suggest a heat-knife first to get a clean non-fraying cut on the Techflex rather than using scissors to cut it. But as long as you aren't doing lots of this work and plan to secure the cut ends under heat-shrink, scissors work fine too.
Helps to be able to place the heat gun so that you don't have to hold it, instead holding the wires and heat-shrink in place and moving that assembly into/out-of the stream of hot air to modulate how much heat is applied and where. IME, you shouldn't need a heat-shield for microphone capsules as long as you are careful to direct the hot air on to the heat-shrink only rather than the capsule, as the air temperature drops rapidly outside the collimated air stream. I find I more often need to use some kind of heat-sink when soldering to limit heat-conductance from the work-area through the wire to plastic bits and electrical components.
IME, standard expanding Techflex is plenty flexible, often far more so than the wire(s) it covers. The side-entry slitted-down-one-side style of Techflex is not quite as flexible, nor as uniformly so, but is easier to reconfigure when necessary. That kind should be cut with a hot-knife as you can't heat shrink the ends and retain side-entry re-thread ability. I've not had much hands-on experience with the side-entry type.
FYI, I'll be posting about the small diameter 1/8" and 1/4" F6 quiet I just received yesterday to repair some integrated mic cables that have crumbling jackets and make some wiring harnesses. It's made from standard Techflex weave material, but the threads have a softer feel to it and produce less abrasion noise.