It feels crass to talk about such things so quickly, but it’s a practical political question, of course. What happens now? The Democratic governor chooses one of three candidates put forward by the head of the state GOP.
Here’s the relevant Wyoming statute:
Wyo. Stat. 22-18-111(a)
(i) If a vacancy occurs in the office of United States senator or in any state office other than the office of justice of the supreme court and the office of district court judge, the governor shall immediately notify in writing the chairman of the state central committee of the political party which the last incumbent represented at the time of his election under W.S. 22-6-120(a)(vii), or at the time of his appointment if not elected to office. The chairman shall call a meeting of the state central committee to be held not later than fifteen (15) days after he receives notice of the vacancy. At the meeting the state central committee shall select and transmit to the governor the names of three (3) persons qualified to fill the vacancy. Within five (5) days after receiving these three (3) names, the governor shall fill the vacancy by temporary appointment of one (1) of the three (3) to hold the office. If the incumbent who has vacated office did not represent a political party at the time of his election, or at the time of his appointment if not elected to office, the governor shall notify in writing the chairman of all state central committees of parties registered with the secretary of state. The state central committees shall submit to the governor, within fifteen (15) days after notice of the vacancy, the name of one (1) person qualified to fill the vacancy. The governor shall also cause to be published in a newspaper of general circulation in the state notice of the vacancy in office. Qualified persons who do not belong to a party may, within fifteen (15) days after publication of the vacancy in office, submit a petition signed by one hundred (100) registered voters, seeking consideration for appointment to the office. Within five (5) days after receiving the names of qualified persons, the governor shall fill the vacancy by temporary appointment to the office, from the names submitted or from those petitioning for appointment;