I had to drill holes so they would fill with water and sink. They still have some buoyancy but will stay in place. So it will depend a lot on your water depth but that goes for whatever lounger you are looking at.
@SyncLock I have about 15.5" of water on my shelf. Do you think the swimways would work on it with the holes drilled?
Do you know the height from the ground to the top of where your knees would go?
Also how deep the plastic is (~5").
Thats on the deeper side of water depths for a shelf. For 15" of water you will find that many options will float because they dont have enough weight resistance once submerged. Ledge Lounger has something called a riser adapter that allows the chaise to sit higher in the water and not directly on the ledge so that the weight still keeps them in place.