You can run with smaller wheels. They do have sets that will fit, but consider the following:
1. Smaller diameter wheels means lower ground clearance.
2. Smaller diameter wheels means lower top speed.
3. The Monster Truck will certainly not look so much like a monster truck with little baby-sized tires on it.
As for the handling question:
1. You will get a tighter turn radius
2. Loss of traction due to the decreased tread-to-ground contact surface area
3. Better stability due to the lower center of gravity and lower ride height.
4. Certainly will hand better because it will not move as fast on the top end.
5. Will lose a lot of its serious off-road capability for numerous reasons.
BUT you will get the "lo-rider" look if you use some chromed up rims and the right kind of wheel. I have seen full sized Suburbans and large SUV type trucks running with what looked like car wheels. Looked stupid as hell in my opinion, but to each his own....