IMO you can have an online relationship, and you can cheat on your partner that way.

Your partner is entitled to feel aggrieved because, if you think you have been cheating, then sure as eggs is eggs, so will she.

But you can keep your little secret to yourself. It's not hard to do. Just get into the routine of closing all windows when you leave your computer. Expect everything you leave on your computer to be read by your partner, if not because she's checking up on you, then because she's just idly browsing. So at the end of your session, delete your files and your history. Deep clean if you have the software.

Final point, if you're caught cheating, are you entitled to be upset that someone's reading your private messages/going online in your name. Is that as bad? Or worse?