I don't think I would use a paper clip.... I generally use one of my *other* nails. Also, I usually use gloves for most household and garden tasks to keep my nails from drying out. It also keeps the dirt out. I use rubber gloves for the wet tasks, and Atlas Nitrile touch gloves for gardening and household tasks.
There are nail care kits in most drug stores that would have an implement intended for cleaning under the nail. Obviously, you don't want something too sharp that might injure the area under the nail where the nail adheres to the skin. Nor do you want something too abrasive that will thin the nail from underneath when you are cleaning.
When the sun shines, bask.
Classical Guitar forever!