Since nerdism or geekery would be the exception rather than the rule, in terms of users' attitudes to computers, any term that describes someone adept at using the tool should suffice.
Use of the term accomplished will convey the meaning they are adept in their use, without implying the user is also a nerd or geek.
adjective
- highly skilled; expert: an accomplished pianist.
EDIT: Since posting this answer the OP has been modified so that the title of the question to specifically precludeprecludes "Expert", which invalidates this answer.