I don't have much time to reply right now, but have been on the Segway tour at Epcot 4 times.
There are no handbrakes. It is primarily controlled by leaning back and forth and shifting weight. If you can only hang onto the control stem with one hand, you may be more unbalanced, but you would be able to compensate for that.
You can go to the Segway website at
www.Segway.com to look at pictures and the owner's manuals. Just to be aware - the last time I took a tour was several years ago and they were not using the most recent models of Segways, so they may work a little differently.
ECVs or walkers are not allowed on the tour. The first half is learning how to use one in a room. Then, you venture out into World Showcase in a group with your tour guide before WS is open to general guests
If you want to try it, I would book the tour, then go to the Segway display at Epcot that was already mentioned. It is a permanent display and was there in April.
They should be able to answer your questions better than if you call and you may be able to try one.
You can always cancel the tour. Although yo can book a tour when you arrive, there are limited numbers of tours each day and each tour is small. If you wait, there may not be any tours with space on the day and time you want to go. Just find out what the cancellation policy is when making the reservation.