The lightest kicking 20 ga semiauto I can think of is the pre-1977 Remington 1100. It was built on the 12 ga receiver so weighs a bit more than many other 20 ga guns. Of course, it would be a used gun and one long out of production but, when they show up, they are really light recoiling.
Otherwise, pretty much any gas operated 20 ga gun will be pretty light recoiling. Beretta, Browning, Remington, and Winchester in both new and used would be where I start. There are other brands that would probably work but those are the better known brands that should have a fair number of options as well as a pretty extensive parts support if needed.
I wouldn't over look a 12 ga either. With light target loads in the 1 oz, 1200 fps or less range, a gas operated 12 ga won't kick much, if any, more than a 20 ga due to the added weight. The ammo can be a little harder to find in the current market but the loads were very common before the present difficulties.This would open up an additional area in your search for a gun and one may find ammo availability to be better as 12 ga dwarfs the rest combined in sales and demand.
