Actually, if you go as far as you can into the corner that the dock creates (the one that's on the side that Kapp'n is not), there is a small area that is a safe zone from jellyfish.
Also, certain hats prevent you from getting a tan, so if you really wanted to avoid it, I'd get some hats. http://merongcrossing.tumblr.com/notanhats Here's a list of hats that prevent tanning, the images were taken down but the names of the hats are still there.