An Arkansas contractor taking work in Wyoming deals with the same four questions everywhere: who licenses the trade, when a licence is actually required, when workers compensation kicks in, and where the business registers. Below is Wyoming's answer to each, with the agency's own link.
Licensing
Wyoming State Fire Marshal's Office, Electrical Board (state); cities and counties license general contractors
No statewide general contractor license; contractor licensing happens at the city and county level. State-level licensing covers electrical work: electrical contractor ($400) and journeyman and master electrician licenses issued statewide by the State Fire Marshal's Office Electrical Board.
Workers compensation
Wyoming Department of Workforce Services, Workers' Compensation Division
Monopolistic: the state fund is the primary provider; most employers obtain coverage through DWS Workers' Compensation Division, required before work begins in extra-hazardous industries; register via WYUI.wyo.gov.
Tax registration
Wyoming Department of Revenue, Excise Tax Division
Excise Tax Division maintains a separate contractor registration and returns section.
https://excise-tax-div.wyo.gov/salesuselodging-tax/salesuselodging-registration
New hire reporting
Most states require newly hired employees to be reported within a short window of their start date.
https://dws.wyo.gov/dws-division/unemployment-insurance/employers/wyoming-new-hire-reporting/
Starting or running the business itself is covered in the contractor business guide. Arkansas licence records for Benton and Washington counties are in the contractor directory.