You dont need a projector (but it helps and is more fun)
If I point my pen at the screen of my laptop iI get almost no reflection at all since there is antireflective coatings...
I set it up at a tablet instead with a tripod to hold the wiimote and a placemat to use as working area

This setup works really well and my son showed his talents right away(ie easy to use)
As the IRpen it sould only be lit when you press a button - not always on or as in some cases flashing...
There is no need to touch the screen at all - I tend to hover a few mm's away from the surface - but on the placemat it works well touching as there is no surface Im afraid to scratch...