Probably not, but it would depend on what kind of letter this was.
The only time you would say, "I won't be doing X" is when there is some expectation, or possibility that you ordinarily would "do X."
For example:
I usually watch Jeopardy every evening, but I won't be watching Jeopardy next week, because I'll be working late.
"Are you coming to the office holiday party this year?" "No, I won't be coming this year."
I'm going on vacation next week and I won't be checking my email until I come back.
If your colleague is reading a personal letter, there would be no expectation that you would read it, so it would not be appropriate to say, "I won't be reading it."
If your colleague were reading a memo that was being passed around the office, then you might say, "I won't be reading it."
As to what you could say instead, there are a lot of options which might have slightly different implications. As this is a somewhat delicate social interaction, choosing the right phrasing might be difficult. Some options would include:
- I wasn't trying to read your letter
- I'm not going to try to read your letter
- I'm not trying to read your letter
- I'm not interested in reading your letter