Personally I think you will cause warpage in it. You are taking off a third (metric third, as well a sae third).
You can get some very good coatings to apply for the bottom or inside. As long as it doesn't see any wear, should look great.
Another idea is to possibly try polycarbonate. May not come in black though. I know it comes in different smoked colors. PET G may be another option. Both it and poly are stronger than acrylic and perhaps a few pence more for PET G and a shilling more for poly. I am talking small sheets. 50 CM x 50 CM. With such a small part, it wouldn't increase your part cost much.