It seems that the wheel encoder caters specifically to the wheel included in the set. If you look at the wheels and the encoder itself, they go hand in hand. The encoder is made to count the spokes on that specific wheel. You may need to find another wheel encoder or make one yourself.
The IR sensors on that encoder simply detect when the light is reflected back. With their black wheel / white spokes it can see the color difference, but with a wheelchair the chrome spokes should
be more than shiny enough to get a reflection. You will have to fiddle with the positioning of the encoder in getting it the right distance from the spokes but it shouldn't be too much of a problem.
There's nothing too special about that specific encoder other than it is packaged up nicely. You could duplicate it with an IR emitter, phototransistor, and a 220R and 47K resistor if you wanted to.