Handling peppers without hurting yourself
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Capsaicin does not damage tissue, which is why the injuries are avoidable and why people take them lightly until the first bad afternoon.
What actually happens
It binds to receptors in skin and mucous membrane and they report burning. Hands are relatively tolerant. Eyes, nose and everything else are not, and hands are how it gets there.
It is oil soluble, so it stays on skin through several water washes and transfers to whatever you touch. The burn that arrives an hour after you finished is usually something you touched, not something you cut.
Gloves, and the mistake with them
Nitrile, and change them. The common failure is wearing one pair through prep, a break, a phone, a face, and back, which spreads capsaicin everywhere rather than containing it.
Take gloves off before you touch anything that is not the work. Treat the glove surface as contaminated, because it is.
For superhots, double glove and wear sleeves. The quantity of capsaicin in a kilogram of reaper is not comparable to a jalapeño and the handling should not be either.
The air is the bigger problem
Blending, simmering and especially reducing a hot sauce puts capsaicin into the air, and a kitchen doing that without extraction becomes unworkable within minutes. It affects everyone in the building, not only the person at the pot.
Run extraction, open what you can, and keep people out. A respirator rated for particulates helps at the blender and does little against steam.
Plan superhot production for a time when the space is otherwise empty. This is a common reason a shared kitchen stops renting to a hot sauce maker.
If it goes wrong
Skin: oil or full-fat dairy, then soap. Water spreads it. Eyes: flush with water anyway, for a long time, and it will be unpleasant and it will pass.
Breathing difficulty, or exposure in someone with asthma, is a medical question and not a toughness one. Know where the nearest help is before you start a superhot batch, the same way you would for any other hazard in the room.