I don't really have strong feeling on
Harrison either way.
As for the nickname
Harry, I think people always forget that they won't be the only ones with an opinion on their child's name/nickname. Eventually, there is a good chance that
Harrison will have his own opinion. So if he doesn't mind (or even likes)
Harry, well then the matter is out of your hands. But while he is young enough, I think
Harry is definitely avoidable. I'd use
Harris as a nickname.