The short answer is that the radiation emitted by the average computer mouse is not enough to be harmful, but you are advised to still exercise caution. The longer answer has to do with where this radiation is coming from.
On a really basic level, it might make sense to ask if everything in your home emits radiation. If you have ever looked at an animated diagram of Earth spinning on its axis or revolving around the sun, then you know that we are always getting hit with particle radiation all the time from cosmic sources like stars and other outer space objects like asteroids and meteorites along with radioactivity often found inside our planet such as Uranium.