They were narrower than the JC boats (just look at the archway they had to pass through by the Castle and it's doubtful that a JC boat would fit). Take a JC boat, take out everything down the middle, and squeeze it together slightly.
The steering was by two steering wheels, actually. Each controlling one of the water jets underneath. (One jet near the front, one near the back)
Here's an excellent article about the swan boats, including photos.
http://www.omniluxe.net/wyw/psb.htm
After re-reading all that, there *was* originally an electric guidance system, but it failed very early on, and thus the dual-water-jet steering was introduced.
-Rob