Don't pull the stripped insulation slug all the way off — hold it while you twist and it keeps the strands together instead of flaring, then it comes off as one clean piece instead of copper shrapnel scattered through the site.
A hole saw without a quick-release mount sits metal-on-metal against its arbor, and repeated heat and pressure can gall the two together until they're stuck. Put a soft copper washer — a flattened bit of copper wire works — between the hole saw and the arbor's base, and it always comes apart easily afterward.