You can remove the heat shields with no problem. Most every 1st gen has them removed now as they rust off.
Also these are not the primaries these are the secondaries. We have 4 cats on these trucks. The primary has to stay as there is an 02 before and 02 after the cat. SOme have removed their secondary cats already but if you are in a state that does emission testing you may have an issue.
You also have only 1/2 a heat sheild looks like you lost the other 1/2.
Also you will want to check out this under your truck too as it will also rust and cause ratteelling. It's the flex joint in the picture below. Looks like a little can.