Since you said "easiest", I would backtrack to the east on I80 to Cheyenne and then loop north I25 around the hills through Casper. It adds about a hundred miles to the trip, but the roads are so much better.
I've seen plenty of snow in WY in May. We were staying in Laramie one time in May for our kid's graduation from UWYO and all the highways were closed and snowed in. We barely made our flight home from Denver.
I've driven a lot in WY and those small roads always take hours longer than the GPS says they will. Their interstates are good though. I think the 25 between Cheyenne and Casper is a great drive.
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