The phrase "markets and fairs" in the first verse surely refers to the annual hiring fairs where agricultural labourers were hired for the next year. These were not unique to North East Scotland but were found all over Britain. These would be an obvious place for recruiting sergeants to target

They would have been if they'd existed. But they postdate the Napoleonic Wars - the feeing fair system only reached its final form when farms began be consolidated into larger units from about 1820 on. Before that, farms were mostly very small family concerns and there was no turnover of labour.

The way military recruitment usually worked in Scotland in the 18th century was that a clan chief or large landowner would raise a levy of men on request. It wasn't done by direct appeal from the army to the prospective soldier. The army didn't have the leverage that a laird's personal authority had on a local scale.