Q. If one sees a sefer lying on the ground, but one’s hands are unclean (whether from food or for some other reason), what should one do? On the one hand, one cannot pick up the sefer with dirty hands. On the other hand, one may not let the sefer lie on the floor while one goes to wash his hands.

A. Horav Shlomo Miller’s Shlit”a opinion is that he should clean his hands with a tissue. If he does not have one available he should use the lower corner of his shirt or similar covered clothing, to wipe clean his hands.
One should avoid touching a sefer after exiting a bathroom or cutting hair or nails etc., even if the hands are not physically dirty, he should wash his hands first, unless the sefer is lying on the ground.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a