Ive never used superglue on a cut, but I keep a bottle of Germoline New Skin in my FAK along with a bottle of wound wash.
This stuff burns like hell for 20 seconds when you put it on a cut, but after that it stops hurting.
I have used it on:-
Paper cuts, grazes, torn quicks, by the nail beds, heel blisters, heat blisters, briar cuts...
I always wash cuts first, then coat it and try not to scream.
Up side is the cuts are imobilised and heal extremely fast and stop nagging at you as soon as it dries - 20 secs or so..
Never had an infection after using it. Touching wood, lol.
Only once have I had a problem with it. My biggest passed me a pair of secoteurs, blades first, and they penetrated through the skin between my thmb and forefinger. I could see the muscles moving in the hole. I washed it out and glued it back together. It healed in days, but the lump of new skin took a few months to grow out.