Wait until he's sleeping and cut his nails then, I've always done it that way because I'm terrified my son will jerk his hand and I'll cut him if he's awake. When he's sound asleep I can do it faster, and he doesn't know the difference. If the nails are even a little bit grown out they will get dirty from lint, saliva, skin cells, and dust. Just keeping them trimmed will help a lot. They grow fast though! I swear, it seems like I trim my son's nails every other day sometimes! Don't worry so much about "washing" your baby's hands. What you are doing is enough, especially at only 11 weeks. We are too germaphobic as a society, and babies need to be exposed to a little dirt every now and again, and unless it's something disgusting like poop, his regular bathing schedule should be adequate.