Tested with one of the 2 pieces of acrylic(it works with both pieces, but it is difficult for one person to hold it all together), and found that a screen is not necessary to refract the light; that is, any object that crosses the path of the IR light will bounce it toward the Wiimote, and it is detected as a tracking point.
Tested with paper alone. The IR LED is able to shine brightly enough through the paper to register on the Wiimote up to 30cm, but when refraction is tried it does not work at all.
Highest distance tested with paper and one piece of acrylic(should go higher with a proper setup and more than 2 hands): 30cm.
Voltage: 9v battery
Number of IR LEDs: 1
Problem: 1 IR LED on 9v only shines far enough to give about 5cm distance in one direction, with about 2 to 3cm to the side. i.e one LED only gives about 25 square cm of 'touchable' space at max. Not very usable for a large screen.
Improvements: Build a prototype setup for more stability and higher accuracy.
Find out the maximum distance the IR light can be refracted till, and which LED gives the highest distance. Also consider ways to power up setup distributing enough power to each IR LED to shine far enough.
Other possible materials: Frosted wallpaper, Tracing paper