I would take 14 through Ranchester/Dayton from Sheridan.
Some safety considerations, the elevation at Sheridan is quite different than the elevation on top of the mountains. You’ll definitely have a steep climb. You will probably go through a cloud transition during the climb with limited visibility and wet or icy conditions. There will probably not be snow in Sheridan but there may be some on top.
When you are almost on top of the hill you’ll run out of cell phone coverage for quite a distance.
I wouldn’t leave Dayton without probably at least 3/4 tank of gas. Knowing me I would fill up in Dayton. But I keep my gas tank pretty full because there’s quite a distance between some towns in Wyo.
From Burgess Junction it’s your choice to take 14 or 14A to Cody. 14A is a seasonally closed road but it’ll probably still be open in mid October. The time difference to Cody between the two is negligible. I usually go through Greybull but that’s because I’m usually going through Greybull for other reasons.
