An optical encoder is fairly simple to add to an existing wheel.
Essentially you mount a photosensor that can detect notches or patches on a disk as it rotates with the wheel. You could use through hole light detection as well.
The circuit design is fairly straight foward
And your arduino program counts the number of pulses it receives. Knowing the number of ticks per revolution, and wheel size, you can get accurate odometry.
Another solution that may work for you is add on encoders for DC motors. Their original intent is to make a regular motor a Servo motors, but would work great for this task as well. The only real difference being that a servo motor uses the information in a closed loop to position the motor, as opposed to just keeping track of it.
And one other solution I thought of - if your wheel chair has spokes like a bicycle, then a magnet like this would be easy to attach, and a magnetic sensor, very similar to the above light detection circuit could be located on the chair/frame. That would probably be the least intrusive to implement. If you needed more than 1 per revolution accuracy, just add more magnets to more spokes, as long as they are distributed evenly.