There are safe ways to solder around PTFE, but they involve things like:
- fume hoods with high volume exhaust;
- respirators;
- gloves;
- soldering at eye level so hot gasses flow up and away from the face;
- low temperature solders;
- precision soldering equipment run at the lowest feasible temperature;
- and absolutely not fiddling while you hover over something, while you try to remove a connection that someone else made, which may involve high temp solder or a good mechanical connection.
People do tend to recover from HF burns, but they are insidious. HF burns tend to show up after a number of hours, and get worse for a day or two. You can read all about it in MSDS. Best to avoid.
And also, I agree with everything @almarg wrote. Leave the RCA wires alone.