Put heat shrink on first. Then make a lineman's splice. If appropriate (solder can cause a stress riser in some cases making vibration problematic) solder. Then slide the heat shrink tube up & shrink it.
Alternatively, use self-vulcanizing silicone tape instead of heat shrink. That stuff doesn't need to be put on first, and doesn't need a heat gun, but is harder to apply on small wires due to the need to stretch it as it's applied.
Don't use the shitty metal alligator grippers you get on "helping hands", they're terrible even when not heating the wire much. A small smooth-jawed vice or two is far better for small work, e.g. a PanaVise model 201.