I got really excited to answer this, because I actually have a case that sounded perfect - the M-Edge Leisure Case. It's got a plastic cover on the front that allows you to see the screen without having to uncover the Kindle. Unfortunately, after some frantic googling, it appears that M-Edge no longer makes this case. However, I had a thought - would a waterproof case work for you? Just looking through Amazon and such, I found a few waterproof cases, that look like they allow you to use your Kindle while it's being protected. This one looks like it would work for a Kindle Fire, as well as the Paperwhite, and the brand Atlas makes a few more expensive cases that look nicer, but will cost a bit more - See Kindle Fire and Kindle Paperwhite.

Hope this helps!