I also am a recent purchaser of a 84 Catalina 27. I needed the winch handles to get the main all the way up when I bought the boat. Now, after having lubed the track as far up as I can reach, and lubing the plastic track cars, I can hoist to the top, by hand, without using any winch. My lines are led aft to the cockpit.
I would get some McLube or similar dry sail track lubricant and go from there.
But, you will need a winch handle at some point in time. Personally, I never use mine, but that is not saying that I won't need it at some point. There are times that I wish I had them, but just wound up man handling it because I couldn't be bothered with the winch handle.
I do feel the pain the next day though! Makes my ribs, back and shoulders remind me how out of shape I am the next day...