How to dispense thick, intense hot sauce without getting residue on the bottle?

I have a bottle of Dave’s Insanity Sauce. I enjoy putting it on my food in small quantities and have no trouble handling the heat… in my mouth. The problem is that the outside of the bottle seems to have some capsaicin residue on it. Even when I wash my hands after handling it, I later experience pain if I touch my eyes or my nose or, um, other body parts.

I suspect the problem is that it’s a thick, viscous sauce and I’m not able to dispense just a drop or two without getting some on the lip of the bottle (where the threads for the cap are), and from there it seems to spread. Is there a good way to 1) dispense sauces like this cleanly, or 2) make the bottle less hazardous?

Washing the bottle with dish detergent may have helped temporarily, but it would be great to not have to do this every time I use the sauce.