To follow up - you can try it before committing to any work.Take your greenland paddle and go to nearest swimming pool, pond, anything where you can sit on the edge right next to the water, and the water level is near the ground level. Simply start paddling on one side (some people will think you are crazy - they give you the same look I get when roller skiing ;-). This will give you idea what it feels like.
Actually, even greenland paddle may provide too much resistance so you may trim the blades a bit.
With proper positioning and proper blade size the feel you get is quite close to the real thing - much better than any machine will give you.
Also, you can consider what I've done - canoe paddling in the racing position (kneeling on one knee) - it uses some of the leg and trunk muscle and is a better workout than regular kayaking. The added plus of canoeing is that you can paddle on the "good" side in order to save your injured shoulder.

: As you said, you can buy a good machine but it will be expensive.
: Here is an idea that many will find hard to believe, but it works and costs
: next to nothing!
: How well it works depends on how exactly you implement it.
: This solution requires a bit of space and a solid foundation - it will not
: work for apartment dweller.
: Imagine 2 basins filled with water to the depth of say, 1.5-2 feet. The
: kayaker sits on a seat (any seat) between the basins and paddles just like
: a regular kayak. The difference is that in a kayak you plant the paddle in
: water and move the boat. Here you are stationary and the paddle moves
: through the water.
: The key here is the adjustment of the resistance level.
: You can use very narrow blade (greenland paddle should work) but then the
: water in the basins need to be fairly deep for proper resistance. On the
: other hand you can have shallow water and have a wider blade.
: You cannot use regular euro blade - the resistance it creates will be too
: much, unless you want strength training.
: Other details to work out is the position of your body and a way to keep you
: firmly in place (so you don't slide when applying the pressure)
: Larger basins are better than smaller, the water will move violently so you
: will need some distance from the water level to the top of the basin.
: Again, all these are details to be worked out.
: I used similar setup many years ago but I used only one basin and
: single-sided canoe paddle.
: Sorry to hear about your cuff. How long ago did you tear it and what kind of
: surgery did you have?