Hello fellow Memphian! I had my last shower at my church. We have a gym and it was perfect for the 40 guests that came. Most churches offer discount or free facility usage for members.
If you are not a member of a church or don't want to have a shower there, check around at local restaurants. Some of them have private rooms. Everyone would buy their own food and you wouldn't have to clean up!
Depending on how much you want to spend there are several locations downtown too.
Hope this helps and Congratulations!!!!