The machine should not be accumulating bits of dough ... it should be designed so that any stray crumbs of dough naturally fall out of it. This is true of mine (Kitchen Aid Pasta Roller attachement) an I merely use a stiff dry brush to clean off the bits of dough which stick to the outside.
If the pasta maker is metal, you definitely do not want to use water, as the instructions say. You will never be able to dry it properly and it will rust.
If it's an inexpensive pasta maker, I would suggest trying a different brand. If it's an expensive one, I would contact the manufacturer. Otherwise, canned compressed air as the two commentors above suggest is worth a try.
FWIW, I wouldn't worry about the egg in the pasta dough becoming toxic. However, I would worry about the dirty pasta maker attracting bugs.