Washing hands for a priest with a bandage

Hello Rabbi,
The laws of hand washing today are strict, so a bandage is exempt from the mentila and only the exposed area needs to be washed with water.

What is a priest supposed to do in the Temple who has been hit and therefore needs a bandage on his hand? (I'm not talking about a broken hand, in which case he is unfit for work, a bandage as a result of a cut or something else)
Will the Rabbis' law apply in such a situation, or will the priest not be able to officiate as long as his hand is bandaged?