If the shower doesn't have a fold down seat the hotel has to have a shower chair no need to bring one.
We were at a major chain once and had a roll in shower I went to the front desk and they told me that they didn't have one and that my DD would have to use her wheelchair to take a shower. I call the corporate office and told them I would put one of their nice chairs in the shower before I put my DD wheelchair in the shower. They put me on hold and while I was on the phone guess what suprise they found a shower chair