You could cut the heatshrink tube, wrap it around the cable and then secure it with transparent tape. It would slide around but at least it wouldn't leave residue on the cable.
Maybe clip-on cable markers like this? [1] Easy to 3D print if you're so inclined.
[1] https://uk.farnell.com/multicomp-pro/pb-250-sm0c/cable-marke...
Visually, if it's something I'm going to be staring at on a daily basis, I like this much better than having tags hanging off of the cable. Tip: consider white-on-black labels.
The labels have been plenty durable in my experience, but if you need extra durability, you could probably just brush some lacquer over it with a Q-tip.
One big differentiator between various Brother models that's not immediately obvious is the tape sizes they accept. The cheaper models don't accept the fatter 24mm/1" labels, gotta step up to the $99ish models for that.