I was swapping over my pigtails and part of the plastic coating around the coax came off.
The coax is still firmly soldered to the SMA connector - is this salvageable with some heat shrink, or do I need a new coax?
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The outermost plastic coating is not too critical; this primarily protects the braid from damage or exposure to elements. For the length involved in your image, you should be fine just adding heatshrink to cover that - and if you extend it over the pin you can get some strain relief too.