Wyoming has no statewide secondhand-dealer or precious-metal dealer law. The state rule most clearly aimed at gold buyers is W.S. 33-6-106: every pawnbroker must record a full description of each article pawned or purchased, the date, the seller's name and address and the amount paid, and keep that record open at all times to any city, county or state peace officer. Breaking it is a misdemeanor (W.S. 33-6-107). The statute sets no holding period, no ID requirement, no age limit and no payment rule.
Wyoming's junk dealer act (W.S. 33-18-101 to 33-18-106) covers anyone in the business of buying or selling secondhand or broken metals, "such as" copper, brass, lead, zinc, tin, steel and cast iron, plus rags, rubber and paper. Gold and silver are not named, but the list is open-ended, so it may reach a buyer of broken gold or silver. A junk dealer records each purchase with the seller's name and residence, checks a federal or state photo ID or notes a license plate number (optional for household items worth under fifty dollars), and keeps the book open to the sheriff and police.
Everything else is local. State law lets cities and towns license and regulate pawnbrokers and junk or secondhand dealers and inspect their premises for stolen property (W.S. 15-1-103), so whether a Cheyenne or Casper shop holds your jewelry before resale depends on city rules, not a Wyoming statute.