Electrical – Is Nonmetallic Sheathed Cable Safe to Touch

Cable installers work with "live" wires all the time. There's no voltage on their lines that I'm aware of, only signal and maybe some interference. You do need to disconnect lines for satellite dishes or mast mounted amplifiers since they may have a power injector that adds voltage into the lines.

When crimping the new cable, make sure the center wire is long enough (you can trim it after you crimp a new end) and get some of metal mesh that forms the second wire in tight contact with the crimped fastener. I usually pull some of that mesh back over the insulation so there's a tight bond when it's crimped.

The derating would only occur if there is a section 24 in. long or more, where the cables are "bundled" together (from my understanding).

"without maintaining spacing for a continuous length longer than 600 mm (24 in.).

If the cables are run through a joist cavity, they'll be "bundled" for 1 1/2" - 3" at the top plate, and 1 1/2" - 3" at the bottom of the wall. Each of which is far under the 24 in. limit. Where the cables dangle through the cavity, they are not wrapped, taped, or bound together. They are only "bundled" for a short distance while they enter/leave the cavity.