One of my high school students asked if someone with a prosthetic hand could be ordained. If so, would that hand be anointed? What if a man was born without arms?
I think that all the things you mentioned are possible. The Catholic Church has established various impediments to ordination, but it can also dispense from many of them.
At one time, a man blind in his left eye could not be ordained because that was his “canonical eye.” The missal rested on a stand to the priest’s left at the altar.
The most famous case of such a dispensation may be St. Isaac Jogues . He was already a priest when he lost several fingers during torture by Native Americans in the New World. Pope Urban VIII allowed him to continue celebrating Mass, noting that Jogues had lost those fingers precisely because of his preaching of the good news of Jesus Christ. Jogues was canonized in 1930.
Canons 1040–49 give an exhaustive list of impediments to ordination as a deacon, priest, or bishop. Some impediments prevent the exercise of a sacramental ministry already authorized.
Neither condition described above is currently an impediment. In some cases, impediments to ordination are reserved to the Holy See; in other cases, the local bishop or major superior for the man’s religious community can dispense from the impediment.
The Old Testament prescribed that only healthy animals could be offered for sacrifice by healthy priests. Physical impediments to ordination arose from one application of that command.