All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad
is His slave and Messenger.
It is permissible for you to undergo that surgery and have that reconstruction, because it is not merely for beautification; rather, it is to remove an obvious defect that has affected the nail. Furthermore, what is covered by the nail does not have to be washed, because doing so is not possible. Therefore, your ablution is valid if the new nail will cover the same area as the original nail used to cover.
Allah Knows best.