You'll be fine. We've been three times and you get a full hour of training before going out into the park. The CMs are great, and if you or they feel uncomfortable at all about how you are doing, they will give you extra help. If after the training you still aren't comfortable and don't want to ride out in the World Showcase, you have the option to opt out.
On two of our tours we've had little incidents where one person in the group had a little spill. Nothing big as you aren't going very fast and you're just a few inches off the ground. Each time was the same cause - not paying attention to where their wheels were and bumping a curb, then overcorrecting with the steering. In one case the person simply stepped off the Segway, and in the other they attempted to do so but didn't let go of the handle and fell to one knee. More a bruise to the ego than a physical injury in both cases. Just pay attention during training and follow the CM instructions and you'll be fine. You'll LOVE it!