People whose limbs have been amputated, generally report of phantom limbs. They even experience sweating, itch etc on the phantom limb. Now how come the brain detects all that on a limb that isn't even present? It seems sense originates in the brain and the body parts are just acting mere like sensors and output peripherals.
If that is true you should not worry much about this biological body thing at all. After all we have organ transplants already. Like the argument about Ship of Theseus, you have to ask if a person who underwent organ transplants for more than one organ is actually the original person. If you were to wake that person post surgery, how much less of his original self he is since a good deal of body parts are replaced I am sure to bet he will say nothing changed at all.
Transferring brain to a computer is just brain transplant. If you accept organ transplant you should hardly have any problem with this at all.