Like most things, canoes are perfectly safe if used in the manner in which they were designed. In actual fact, you have to work pretty hard to flip a canoe over because of its relatively flat bottom. Granted, if you stand up in a canoe, it is likely to turn over but then again, you're kind of asking for trouble if you do something like that.
Steering a canoe efficiently can cause quite a bit of frustration for the novice canoeist. The best advice is to do a little as possible and when you do need to correct the course, do it with the least amount of effort. This will ensure you don't get stuck in a cycle of overcorrecting yourself.
The short answer is yes, you can paddle a canoe by yourself. It is infinitely easier to do with two people but with a few minor alterations, you should be able to have a pleasant journey.
