I tried a DecalGirl skin, which while attractive, did not really solve the problem for me. Since I usually read in bed while lying on my back, I just found the shape uncomfortable to hold even with the skin. Quite often, my hand would ache after a long reading session because I was gripping the device so hard in order to keep from dropping it.
I ended up buying this
MoKo case, and I'm very happy with it. I hold the Oasis with the cover folded back behind the device, my index finger between the covers, and my other three fingers behind the cover, supporting the device. My thumb rests lightly in front to press the page turn buttons. This method works for me whether I'm holding the Oasis in my right or left hand. Yeah, it adds a bit of weight, but together the Oasis and case weigh 319 grams, which is still lighter than my PaperWhite in its official Amazon case. As always YMMV.