Benzoin Tincture. A little $5-10 bottle will most likely last you the rest of your life. If it ever dried out all you would need to do is add some alcohol (rubbing alcohol or ethyl alcohol if apocalypse) and it's good to go. Easiest way to apply it is get a qtip and pour the benzoin dropwise until the tip of the qtip is reasonably saturated. You can actually reuse the same q tip probably a dozen times after you soak it once, just need a few drops of rubbing alcohol on it to reliquefy the benzoin.
Bandaid will not come off until you want it off. Or maybe after a few weeks when your skin finally fully sheds its outer dead layer, but I haven't kept a bandaid on long enough to check that.
Wounds actually heal faster when they're kept moist. A little bit of vaseline or triple antibiotic (usually not necessary but is an option) on the wound + bandaid = fast healing wound. The idea that cuts need to "air out" is a complete myth and it really fucks up healing and causes scarring.