I don't think you should be scared to replace a coaxial line. its not even hard line. just get good coax from pasternack or something
it might be a little expensive but that insulation is BS and should not be kept around
get the OD crimp tool, solder interior pin (preferably with hot tweezers or hot air not to get solder on the connector) and remake the cables if you can't buy something close enough ready made. the only thing it is is a bit expensive.
I replace things like this but with not cheap brands.
What is to say the dielectric in the cable is in a good state if that happened to the insulation??
if you simply cannot afford it, buy very high shrink ratio heat shrink and recoat it. might take trial and error.
just be warned replacing the cable takes some planning and engineering, you can't just wing this