I wouldn't hesitate to go through both states in mid-October. IF a winter storm hits, worst case scenario - you stay in an RV Park for one or two days. Most likely is that you'll have beautiful fall type weather, especially on the Interstates and main highways.
Live a little and get your new decals. We had truck chains for our Alaska Highway November/December trips and didn't use them. Never had chains for the trailer (20' cargo).
Don't buy chains for an "if" when you can take a day delay.
Oh and we have running water in our homes in Wyoming now! ;)