It is fairly safe, but you still have to be aware of your surroundings, watch your stuff, carry your bags close to you (lots of grab-and-run type of theft in the City), trust no one -- common sense.
The water taxi terminals are in the downtown area of the City, close to where the cruise ship visitors come ashore. On cruise ship days, the area is patrolled by the police.
However, do you have to use that water taxi service?
If you miss the 12 noon boat (which I would doubt), there are 2 other services with boats departing before 3pm. And there are flights.
Here are the links to the 3 water taxi services' websites where you can find the schedules & fares:http://www.cayecaulkerwatertaxi.com/schedule.htmlhttp://belizewatertaxi.com/rates-schedulehttp://www.sanpedrowatertaxi.com/index.html