No, I'm saying you can use one or the other... Either the drain-wire exculsively, or the strand-wire shield exculsively. When I said "parallel", I was just letting you know they run-along next to each other, touching each other, all along the snake.
Usually, you'd use the drain-wire if crimping or the strand-wire shield when soldering. I was just saying I've used the drain-wire to solder to connectors plenty of times, just because I wasn't thinking...
Whichever you're not using (the drain-wire or strand-wire shield), you can just cut it off while you're prepping the ends.
I assume you remember the shield goes to pin 1/ sleeve (XLR/ 1/4" TRS)? Or was that what you were asking in the first place? Anyway, you can "lift" it if you'd like to help avoid ground-loops; some gear don't like that though. You can do this at the input or output of your gear, but the key here is making sure either the input ONLY or the output ONLY... Another words, make sure you're 100% consistent. Now days, most people choose the input, yours truly included.
Yeah, if you could use my snake, let me know.