Why shotguns would not transform Trafalgar

Would a shipment of double-barrelled shotguns and buckshot have changed Trafalgar for the Franco-Spanish fleet?

Only at the margins in close boarding; limited shots, slow reload, smoke, and cannon effects prevent it from changing the battle as a whole.

Buckshot would be brutal at close range, especially during a boarding action. A double-barrelled weapon still allows only two shots before a lengthy reload. It cannot penetrate decks and would add little once cannon fire had already swept an exposed deck. If boarders had broken into the ship through gunports, defenders would have little time to reload. The weapon could change individual encounters without altering Trafalgar's operational result.