It's possible to take the tip off the cutting and graft it back onto the mother plant. The main thing to ensure is that the central vascular bundles of the two parts overlap. Consult a cactus grafting guide for more details. So you could repeatedly take out small slices over time and end up with a cactus that looks like a stack of green cookies. Thinnest I've successfully grafted was 10mm - as a slice, not a tip, but that slice included a small sprouted stem.
Even without doing this, the plant sprouts new growing tips, often more than one.
The idea of peeling strips is intriguing and might lead to increased potency in the mother plant. The downside would be impaired aesthetics, and possibly increased risk of rot.
Frankly though, if you're fiddling around with prickly cacti you might as well just cut big bits off, then trim off the tips for subsequent rooting as cuttings. Your cactus collection will then slowly expand exponentially. Beware - this hobby can end up taking up quite a lot of space!
Grafting is strangely satisfying though, so I'd say give it a try.
βThere is a way of manipulating matter and energy so as to produce what modern scientists call 'a field of force'. The field acts on the observer and puts him in a privileged position vis-à-vis the universe. From this position he has access to the realities which are ordinarily hidden from us by time and space, matter and energy. This is what we call the Great Work."
β Jacques Bergier, quoting Fulcanelli