Re the relative safety of the various grades of superglue, my understanding is that they are all cyanoacrylates but with slightly different molecular structures that give slightly different properties - rate of curing, stability, adhesive power etc. The key difference for dealing with wounds is their relative rates of degradation and release of formaldehyde / methanal. Bostik / Gorilla Glue etc form a stronger, harder bond than the veterinary / medical grade variants, but breakdown faster and release more formaldehyde.
Formaldehyde is a carcinogen but considering the amounts concerned and the length of exposure, I suspect the more realistic risk is irritation / inflammation of the wound. Incidentally, formaldehyde is hard stuff to avoid - it's given off by burning lots of fuels, and leaches from construction materials like foam insulation, plywood, particleboard etc. Personally, if I felt glueing would help get me up a problem, I would not be too concerned... but then I had a decade in a lab that was awash with PFAS, have spent the last decade exploring fire scenes potentially containing asbestos, and drink too much. So, figure glueing splits would be last in the queue of "activities that will be implicated in my death". YMMV!
That said, I personally avoid gluing tape to flesh, just because of squeamishness about removing it afterwards. I use superglue but apply it between the layers of wraps e.g. where "figure 8s" cross themselves and to anchor where the wrap ends - maybe not as secure as gluing to skin but appreciably reduces slippage and makesthe tape job last longer.