What I'm about to suggest is a lot Rube Goldberg... but may appeal to anyone not confident of something more invasive or permanent.
At the ned, I have a second, more sensible, suggestion.
The Arduino could be programmed to turn on a "mouse shaker" or "button presser".
The user of the Arduino+sleepy PC system would have to remember to put the mouse on or in the shaker/ presser when going away and wanting the "wake up" system active.
As I said... yes, "Rube Goldberg"...
... but, from reading many forum posts, I know it will appeal to some!
If it is an optical mouse, and you are sure that the mouse doesn't go to sleep until a button is pressed, a simple "fan" mounted inside a clear box, with a place on top for the mouse to sit where the fan blades are "in sight of" the optical sensor, should do the job. The moving blades will "look" like a surface moving by under the mouse?
For a "wiggler", just set up a small motor with a badly balanced weight attached to the shaft.
More sensible "answer"?....
For what mice cost, I'd be inclined to open one up, attach two wires to one of the button's switches. Those wires would then be taped along the mouse's original wire, and taken thus to some place out of the way of the mouse's normal use, and the Arduino can be programmed to "connect" those wires, thus imitating a mouse click with minimal invasion of hardware, complexity of construction, or inconvenience in everyday use of computer either for general purposes or for whatever you want to wake it for.