They should be fine.

Give the top of the cotterpin a gentle tap with a hammer and tighten the nut snug but don't overdo it. The taper holds the crank on, the nut holds the cotterpin in. They can't go anywhere unless unusually loose.

Removing them is not usually a big deal, but many times requires new cotters, and the taper has to be filed to fit.

After that, the bottom bracket services like any other cup, spindle and bearings one, requiring somewhat specialized tools.