It's as dangerous as crossing a busy intersection can be.
Straights for sale here:
Worst two injuries I've had was an about 2" long slice on my jaw from being careless, and a large welt literally shaved off (had let a full beard grow, had an ingrown/bugbite/pimple I hadn't noticed, cut it clean off... resulted in a pretty big scab). Neither left a scar. The slice stopped right away with a styptic pencil, the chunk would have hurt like HELL to styptic so I just applied pressure till it stopped. Typically razor injuries aren't too bad since they're clean (very sharp) and not deep (You never hold the razor in a way it would cut deeply). There's definitely potential to hurt yourself, in the same way that holding a loaded rifle at the range has potential to hurt yourself. Lots have things have potential for whatnot, "has potential" doesn't mean "likely". Be careful and don't do anything stupid. As others have said, DE's give me way more bloodletting than straights ever have.
I switch between straights and double edge razors. My worst cuts with the straight came when I used a square point blade and the tip caught my ear lobe. Use a curved point when you begin and you probably won't have that problem.
I've been using a whippeddog for 3 weeks now and I'm still here.
As others have said, start with the cheeks. The three elements of having with a straight are lather, stropping and actual shaving. Good lathering and knowing your beard growth pattern you can learn with a DE, stropping and stokes with a straight you have to learn as you go with the straight.
I have had no more nicks and bleeders than with a DE, but keep a shallow angle between blade and your skin. There is a type of injury I got to begin with I don't think you can get with anything but a straight; trying to adjust the angle with the blade still on your skin is not good, if you get too steep the weight of the blade alone can be enough pressure to cut through the epidermis. It doesn't bleed much if at all, but it looks like a dead straight paper cut on you face. I did it a couple of times the first week; I couldn't decide if I looked more like a Bond villain or a Prussian duelist.
One thing that I found, that may not be the case for others, is that some days the left hand works and some days it doesn't; and I just have to give up on it and do everything with the right.
It's worth it just for the experience, it focuses the mind extremely well. You know the old saying to do something everyday that scares you? Now you can do it before you leave the bathroom in the morning .