12" is a good size, as the tires are available and it can still handle bumps.
The little ones from Unicycle.uk.com should be great fun, but will wear you out in a parade.
Yes, there is a limit on useful wheel size. It depends on how hard you want to work, and how much discomfort you want during a parade.
My old unicycle club, Redford, had a couple of mini-giraffes. One had a 4" wheel, probably similar to the Fleet mini-giraffe. It was geared up to go at a decent speed, but of course you felt all the texture of the road. If you got this unicycle going in a spin, it was really hard to get out of it. The thing was spin-crazy. And bumpy. Watch out for cracks, potholes, rocks, and the ever-dangerous horse manure!
We also had a small giraffe with a wheel about 1.5" in diameter. This wheel was made of steel, and had to be ridden on smooth pavement only. You would never survive in a NYC parade, for instance, because there is too much variety in the riding surface. You’d have to stop for every seam in the pavement, and tiny rocks would lock you up. Definitely not recommended for parades.
As for a big wheel, it would be very visually interesting. I don’t think I’ve ever seen a giraffe with a Coker-sized wheel or larger. The cycle would be very heavy and hard to steer. It would be unsafe to idle on, unless you lowered the gear ratio. It also might be a big pain to transport, as the wheel size plus frame sticking out will take up a lot of space. Minimum height for a Coker giraffe, without lots of engineering, will be close to 6’.
For very short parades, the Fleet giraffe will be fun. For anything longer, or if you want to worry less about seams & cracks, try a 12" wheel.