If you have brakes, then a fixie is no more dangerous than a single speed once you get accustomed to not being able to coast. Simply put, on a fixie, if the bike is moving, you must be pedaling. Take it easy at first and you will adapt to this quickly.
I would recommend spending a bit of time where there isn't other bikers/pedestrians when you first ride as a fixie.
I would recommend starting with a flip-flop rear wheel, fixie on one side and freewheel on the other, and carrying a 15mm wrench so you can flip it. As you start out on a fixie it can be more taxing on your legs than you might expect at first. Being able to change over to a single-speed (freewheel) and give your legs a break can be very important.