A solo is definitely less stable...at least as far as initial stability...but at least on my Bell Magic the final stabilty is pretty good.  That is to say that it wobbles a lot easier than a tandem but it's not as easy to capsize as you'd think.

Main thing you need to remember is to stay centered...or as Magicpaddler will tell you "keep your mind in the middle".  That means if you keep your head over the center of your canoe and your body perpendicular to the horizon that will make it difficult for you to move your center of gravity far enough off balance to cause a capsize.

A couple years back I rode a fully loaded Wenonah Advantage parallel to the waves thru 3' rollers across part of Basswood and made the crossing.  I was an idiot to begin the crossing at all, but once I was in it I was committed as executing a 180 was a sure dunking.  I kept my butt loose and my body perpendicular regardless of how the canoe rolled beneath me.  And prayed.

What I like about a solo is that it really feels like an extension of my body in a way that I've never felt when paddling a tandem solo.  Initially it's a little disquieting but in less than an hour you'll begin to feel comfortable.  In a couple of days, you'll feel free!