The spring doesn't need to be a regular
coil spring like would be in a pen. It
can be conical shaped so that when it
is compressed it looks like a spiral.
If you are creative you can make one
by bending a piece of music wire into
a spiral and then stretching it to the
cone shape.

You can also use a piece of flat spring
steel, like is on the clickers and other
noisemakers you see on new years eve.
Cut a piece the size and shape you desire.
punch a hole to fit your axle. Then give it
a slight bend to make a nice smooth curve.
(If you have a hard time visualizing this think
of a bent penny.) If the edges cut onto your
wheel, bend the very edge back a little to
make a slight lip. This spring will take
VERY little space.

Another good source of material is the "slap
bracelet" if you can still find one.

Jenny