You can certainly shoot trap with a 20, provided you've got a fairly long (28") barrel and modified or full choke. If you can find one (they're not common) I would think an improved-modified choke would be best.
I started out shooting trap with standard 12-gauge, 1-1/8oz loads of #7-1/2 shot. Once I started reloading, I went to 1oz loads of #8 shot. Could still break 25-straight, and it was easier on the shoulder. You can easily duplicate that in a 20, and the gun might be easier for you to handle.
Hope this helps you.