I assume this *should* work with PC monitors, as it works with TV's and arcade monitors.
Just swap the yoke wires and you will get a mirror image.
Either swap the vertical or the horizontal (but not both, that'll just "rotate" it upside down).
(standard monitor warnings here: only do this if you know what you're doing and can risk damaging the monitor and know how to do it safely)
Basically the vertical windings are the yellow and green wires, the horizontal are the red and blue.
To reverse the image either:
1) Take the yellow wire and attach it to the post that the green is on and vise-versa
-OR-
2) Take the red wire and attach it to the post that the blue wire is on and vise-versa
This will cause the image to draw backwards, perfect for reflecting in a mirror.
(This is how you can convert a real Kickman board to draw on a "normal" monitor cabinet since their original cab has a mirror in it)
Note: I've tried this with TV's and arcade monitors and it works great. HOWEVER, I have never tried it on a PC monitor (the wires are likely soldered instead of removeable from the posts) and there may be color purity issues with it (therefore I'd be more apt to swap the vertical windings instead of horizontal, but try either and see what the results are and report back)
Otherwise, no, I do not know of software that will mirror the screen. However there may be something available as Arabic screens (windows itself!) will draw backwards.