+1 on what battue said. A 20 will normally recoil worse than a 12 with the same shot payload as 20's tend to be lighter.
I would look at a 12g semi as a first option. The newer Berettas have the 'Kick-Off' system which in conjunction with the in-built recoil reduction of a gas operated semi (actually not a reduction, just spreads the recoil pulse out over a longer period of time) might be the answer for you.
Second option would be a light (7/8 oz) 12 g load at 1150 fps in your current gun - but you say that you want to go lighter, so that option might be out.
Don't go light weight 20g and expect it to not kick unless you go right down in shot payload.
