Our KZ owners manual actually says to use liquid Drano. They wouldn't say that if it could potentially damage something. Have used it twice in our black tank and no issues afterwards. Liquid Drano will not damage plastic or metal. For bad clogs and holding tanks, it's the best thing going.
Drano info. If using a competitor's product, make sure the label says it will not harm metal or plastic.
I thought there is usually an access cover for a shower/tub. Ours has a twist off cover. Our old TT had about a 4x4" cover made from luan plywood on the side of the tub. If you have a cover you can pull the P-trap out and clean it.