Sully -
I haven’t fished the Snake in WY, but I have spent a LOT of time on the Henry’s Fork and the South Fork of the Snake in Idaho.
Since you mentioned throwing a squirrel, this streamer - the Pine Squirrel Cheater - is probably just what you are looking for. Don’t let the simplicity fool you. It has taken trouts everywhere I have fished it in Idaho and Montana.
http://www.flyanglersonline.com/flytying/fotw2009/fotw20090921.php
Another good fly would be Scott Sanchez’s “Double Bunny.” If you are not familiar with Sanchez, he is one of the most creative fly tiers in the Intermountain West over the past twenty years or so. The “Double Bunny” was barred from the One Fly Contest on the Snake after it took the title three years running back in the '90’s.
The “Double Bunny” is an easy fly to tie - a couple strips of rabbit zonker, some crystal flash, and, if you want to be fancy, some eyes and epoxy. I’ve fished the simplified version on the South Fork and done well with it. I like an olive over white streamer, but brown over yellow is also a great combination. You should be able to find a recipe and tying instructions for the bunny if you google it. If you have any trouble, let me know.
On the smaller side, another effective streamer I’ve used on the South Fork is a Thunder Creek Minnow. Basically bucktail in your choice of color. I liked a black over olive over white combination. Again, if you google Thunder Creek Minnows you should be able find a recipe and tying instructions. There is one in the old FOTW archives, can’t remember when, but look for something like Little Brown Trout Streamer. If you can’t find it, let me know and I’ll take a look.
Another fly which should do well, on top, in August, is the FEB Hopper. That is a simple hopper pattern that has been really good for me and everyone else I know who has fished it in the Intermountain West, including some of the famous rivers of YNP. I think it gets taken for a golden stone almost as much as a hopper. Follow the link for the FOTW on that fly.
http://www.flyanglersonline.com/flytying/fotw2/fotw20090810.php
John