I receive more calls from potential clients with your situation. The facts are you know you need surgery. While you can do your job today, you do not know when you will not be able to due to the torn rotator cuff. If you are forced to do the surgery later because you continue to work, the recover and possibly multiple surgeries are guranteed to keep you out of work for more than four months.
What happens if you get terminated due to economic reasons? Now you have let the statute of limitatiions run because you could not take the time or reduction in pay to have the surgery and now you will not have a job or any income, can not get hired for a new job because you need surgery and can not afford the surgery.
Your getting the rotator cuff repaired is your best bet for the long term solution. It may be difficult during the surgery, but now you have the ability to get the surgery paid for, that option will not remain open forever, and your job may not be there forever either. Think long term and I think you can see what is in your best interest. A tough decision no doubt, but one that needs to be made.