Question:
When washing hands on Shabbos, does one have to be careful that no water should get on his clothing/sleeves, due to the prohibition of laundering?
Answer:
Not a problem because he has no intention to wash his clothing and it is not inevitable (psik reshe) that every time he washes his hands his clothing will become wet.
Sources:
O:CH 314:1, 320:18, 336 Mishnah Berurah 25
