I've driven the road to Cody a number of times and don't recall any major steep grades. But I am not very sensitive to road grades unless they are very steep like Hwy 12 in UT. You do drop about 3000 feet between YNP and Cody tho, so there have to be grades. There is some way to show grades on Google maps but I don't recall how. The road around the dam just before you get to Cody is somewhat curvy as I recall. There is a small museum there which is worth a stop.
The diversion to I-90 is -way- out of your way and will add hours to the trip.