If you cannot get your chambers measured, 2 1/2" would work. No need for the added expense of 2 inch shells. I'm not sure when Parker started boring 2 3/4" chambers, but your gun would be close to that timeframe. Generally, they had 2 5/8" around the time of your gun, but to be sure, you should get them measured. Galazan sells an inexpensive drop-in gauge, and since you are bound to add to your collection (
), you'll eventually need one.
As already recommended, lighter loads with moderate speeds should be okay, assuming your gun is sound. Many older guns have had things done to them over time, as I'm sure you know, so getting a good, qualified appraisal is important.
Good shooting with your new Parker. Post some photos of your gun and some of the game you shoot and places you hunt.