Learn English – The proper way of asking this “would you mind…” question

Your answer is perfectly fine. Why do you want to change it?

If you are concerned about politeness, I suggest you give a reason why you do not want this person to use your computer. For example,

"I'd rather you didn't, if you don't mind. The last person who used my computer spilled coffee on the keyboard!"

Or,

"I'd rather you didn't, if you don't mind. It's just a personal policy of mine."

If you change the wording, you could include the words I'm sorry,

"I'm sorry, but no. I hope you don't mind."

The hope you don't mind expands the thought of your being sorry. In effect, you are saying that you do not want to offend this person, you are sorry if you do, but your answer is nevertheless no.

Your tone of voice is important. Your facial expression is important, too. When you are telling a person "No," your voice should be pleasant and conciliatory, and your face should "wear" a partial smile.

Another possibility:

"I do not want to offend you, but I'd rather you didn't."

Or,

"Please don't take this in the wrong way, but I'd rather you didn't. It's just a personal policy of mine."

This response assumes the person could be offended, but it tells him or her that that is not your intention. In other words, you would say no to anybody and everybody, not just him or her. Or,

"I'd prefer you didn't, if you don't mind."

Or,

"Please understand, but I'd prefer you didn't."

Or,

"I hope you understand, but I'd rather you didn't."

Or,

"No offense, but I'd rather you didn't."

Here, the phrase "No offense" is shorthand for "I do not mean to offend you" or "My intention is not to offend you."

Long form: Thanks. Feel free to contact me as well if you have any questions.

Short form: Thanks. Same to you. (assuming the forum is an informal environment)

However, on many forums, you might want avoid such chit-chat since it's implied in the forum environment.