Any animal that eats other animals is potentially a hazard for rabies. 'Coons are carnivorous, and are "opportunists" when it comes to eating carrion. 'Coons and 'possums are particularly prone to carry epizootic diseases, transmissible to humans, because they frequent and eat from "human waste dumps" where they can pick up such stuff. Trichinosis is not unknown in both, and there have been reports of tularemia although I don't know that that's been confirmed in 'coons. Fleas, ticks, and other parasites are also common in almost all fur-bearing animals, some of which can leave vermin behind even if you get rid of the "bearer."

My own experience is that if the critter has decided his "home" is in the basement he's unlikely to follow a trail of food out. It can be tried, but I wouldn't hold much hope for it. If it works, someone has to be present to slam the door pretty quickly to keep the critter from just strolling back in.

Recommendations about "sticky foods" for bait indicate a shallow understanding of the Havahart traps. The bait is placed inside, so that the critter has to get far enough in for the door to slam shut, so sticky isn't really the solution. 'Coons have been known to reach through the trap mesh and move the bait to where they can get it without entering the trap (usually if they've been trapped before) so tying it down inside of the trap may help.

You might just try making his chosen place "less comfortable." He probably chose the basement because it appeared to be "remote," so loud music, moving stuff around, banging and clanging might influence him to find someplace quieter; but it's likely to take a while and more likely to drive the family bezonkers than to be successful. You might just find that he likes Rock & Roll. 'Coons can be remarkably tolerant of close "human presence" and traffic if they feel hidden enough.

An old Red Ryder style BB gun (spring type - not the pump up or CO₂ pellet kind) would be unlikely to hurt him badly enough to hinder his survival, particularly through the thicker fur; so "pestering him" by taking frequent pot shots might persuade him to move out - or might just make him mad. Not really a method to be recommended.

John