With a bad shoulder, you want to minimize trauma to to your joints, that is a smaller blade to slip a bit in the water under effort, and/or a more flexible shaft. Note that oval shaft are stiffer than round ones. Lighter paddles are also a great way to reduce stress. If you get a sore back, try to bend your knees more, and lower your upper hand compared to your shoulder.
"cupped" paddle blades are grate for surfing as they give a very positive grip. Strighter paddles are more efficient at entering/leaving water and thus better for racing / touring. Slightly cupped design work great in both cases :-)
"It also pulls the board off target after only a couple of strokes" is only technique. Try to understand the physics of it at:
www.standupzone.com/forum/index.php?topic=15897.0 to practice. After some time you will be able to aim the board left or right without changing paddling sides.
Also, be careful to have the shaft vertical:
This will get you row:
This will counter the row, and even give you anti-row:
