The shock should be mounted to brackets which in turn are welded to the plate. The brackets should be 3/16" and thus the plate should be as well. As for strength, 3/16" plate on edge is a LOT stronger than you realize. The brackets apply the force against the plate, which will be welded to the underside of the seat rails (if I understand you correctly?) As long as the plate and brackets are properly welded, I think you'll be safe.
If the plate and brackets are 1/8" you're probably on the borderline of strong enough. And a lot of really depends on how the shock is designed and mounted. Some act as dampers on pivot arms, some are direct to frame. But the shock itself takes up a lot of the force that would be otherwise transferred to the frame. This is not an inducement to short cut safety, just an explanation.
I'd defer to whomever is building your monoshock for their guidance as a final judgement.