Trying to talk him out of his delusion is not going to help, but you don't need to fully "go along with it," either. I would try to find some middle ground of talking about the reality of the situation but without starting an argument. You don't have to do anything more than just mention certain things in passing. It's best not to be confrontational. Be calm, and don't feel as though you have to convince him of anything, but keep yourself grounded in what is real, and let him see that. The thing that will probably help the most is for him to get out of the hospital and back into a familar environment, so I hope that that is going to be medically possible. You haven't mentioned what kind of surgery he had or what his prognosis is, but if and when he is able to come back home, his thinking should clear up a lot. With older folks, this kind of post-operative confusion is pretty common. The fact that he has already improved so much is a good sign. Best of luck for him to have a full recovery.
I had brain surgery 25 years ago and we were sent home with NO help. Brain injuries were not known about then. Now, if you research Google with the term "Acquired Brain Injury' which is the kind of injury your father and I have - it was acquired through surgery not an outward force - that is Traumatic Brain Injury. Search for either of these injuries - symptoms etc., are all the same or relatively similar. You will find LOTS of information. I was told that sites from the United Kingdom and Australia are very up to date and on target. I wish you and your dad well. I am 25 years post-op and still learning and love to help others struggle.