727 shift cable housing repair

:banghead:

When I built my '62 Valiant V8 conversion, I screwed up: I ran the 727's shift cable too close to the exhaust, and it burned a hole in the outside rubber sleeve. Now ATF is leaking out of the cable onto the exhaust, making clouds of smoke. A friend of mine at a transmission shop told me I should be able to remove the transmission end of the cable, clean up the burned area, slide some heat-shrink tubing over it, and hit it with a heat gun to seal the hole. Does this sound feasible to you? The largest heat-shrink tubing I could find was 3/8" diameter, which is larger than the cable housing itself, but will it fit over the tranny end of the cable? Thanks in advance for your advice. Bill Crowell