You probably won't be able to catch every single one that he loses. My puppy has lost quite a few, and I've actually only seen about 3 come out, and I watch him like a hawk. It is safe for them to swallow them, they are so tiny it is unlikely that the puppy will have any trouble passing the little teeth.
I haven't seen any blood... although one of his stuffed toys had a touch of pink on it the other day, but no biggie. His new teeth won't be as sharp... but you do want to teach him NOT to bite, because as he grows he'll have a much more forceful bite. Don't take your chances with that one :D
What I do for my pup, to ease his teething pain, is take an old sock or dish towel, run it under water, and put it in the freezer for a few hours. The cold helps to soothe their sore gums, and most puppies love to sink their teeth into something soft.
Good luck with the pup!