I do this too. I actually keep a pair of metal cuticle nippers nearby for just this purpose. Using those means that I get a cleaner cut and am less likely to bleed afterwards.

I also have some chain finger toys. It’s a small ring sized circle of bike chain with rubber on each section. You can put it on a fingertip and roll it around. It puts pressure on the cuticle area and gives a sensation which fills the need for stimulation in that area without ripping off skin.