If you go to some of the main air gun sales websites (pyramid air, airgun depot, top airgun, etc.), you can read up on various foot pumps and their reviews. You can also read the reviews for different foot pumps on Amazon, etc. With a torn rotator cuff, you wouldn't be able to operate a break barrel gun or a foot pump as both usually require a certain amount of strength through your arms and shoulders. Calling it a foot pump is actually kind of misleading as you out you feet over the feet at the bottom of the pump and push down with your entire upper body. Think of a bicycle pump where you're pumping to a pressure of 50-100 PSI and then imagine pumping an airgun to 3,000 PSI. You get the picture.
from what you posted earlier, it sounds like a break barrel with higher power (25-30 #'s) would serve your purpose and stay within your budget. If you want to buy one, now is when most of the sales ocur. Before you buy, check out reviews on several websites and ask a few google questions so you can get a good idea of what to expect for quality, power and effectiveness in killing rocky raccoon. It's just about guaranteed that somebody somewhere has tried to kill a raccon with all or at least most of the break barrel airguns you're going to consider. might as well benefit from their experience.