I wondered if your cockpit would make it difficult to hold your paddle in the proper position. But you can go kayaking alone, because you'd have to lean pretty hard to swamp a rec boat like you and I have. And, depending on where you go, if you did manage to swamp the boat you could just swim and pull it to shore, then drain it and get back in there. You may not want to go out in the middle of the Chesapeake alone, but there are plenty of other places where you definitely can.
Did REI mention the paddle sling? That's one of the options that Potomac Paddlesports showed us.