If you don’t want to rely on Shanks’ Pony when in Venice, you need a boat. There are water buses and water taxis, and gondolas of course, and many Venetians own their own boat
If you had wheels in mind, however, think again. There are a few concessions to wheelchair users, but they are few and far between. Anyone relying on a wheelchair or other wheeled assistance will find the place inhospitable, I’m sorry to say. It is not due to unwillingness on the part of the Venetians, though, it is down to geography. The streets are often narrow and although it’s a great place for walking, any trip on foot requires passing over a vast number of bridges, the majority of which contain steps. After leaving the bus station the only wheels I saw in Venice were in this poster.
Once you get out to some of the islands though, things change a little. Passing Mazzorbo on board the number 12 waterbus, one of the first things I spotted was a bicycle parked outside a house.
On multi-coloured Burano, there were more, including this suitably colourful one.
My advice, then, is pack comfortable shoes, research the boat routes and, if you use a wheelchair, plan your trip meticulously (and take a strong friend to help you over the bridges!)