May our priest replace the foot washing with hand washing on Holy Thursday?

Hand washing on Holy Thursday is not part of the prescribed ritual and is not permitted by liturgical norms; it is an invention. Canon 846 §1 says the approved liturgical books must be faithfully observed, and no one may add, omit or alter anything on his own authority.

The rite reflects Jesus' command at the Last Supper, and Jesus did not wash his disciples' hands. "So when he had washed their feet [and] put his garments back on and reclined at table again, he said to them, 'Do you realize what I have done for you? You call me "teacher" and "master," and rightly so, for indeed I am. If I, therefore, the master and teacher, have washed your feet, you ought to wash one another's feet. I have given you a model to follow, so that as I have done for you, you should also do'" (John 13:12-15). When Peter protested, and then asked Jesus to wash his hands and head too, Jesus said that one who has bathed needs only his feet washed (John 13:6-10).

Paschale Solemnitatis (51) says the traditional washing of the feet of chosen men on this day represents the service and charity of Christ, who came "not to be served but to serve" (Matthew 20:28), and that this tradition should be kept and its meaning explained.