I think it is wonderful that you care enough about the lake to ask this question!
Your outdoor shower should have some kind of gravel pit below it for all water to collect and seep into the ground properly with no runoff. If you were not using soap products in the shower I would not worry about anything as you are simply rinsing off and no difference between that and swimming in the lake.
With the above being said, we also have an outdoor shower and use it quite frequently. We supply and only allow environmentally neutral products to be used in it. As a matter of fact, we only allow and use these products throughout our island home and have the below notice posted in all of our bathrooms, laundry room and outdoor shower. We also inform any overnight guests ahead of time.
I think in your situation, it may be best if you supply the products to your renters and stock the outdoor shower with them. They are not very expensive...
Good Luck!
Dan
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It's Always Sunny On Welch Island!!
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