You specifically mention Scotch whisky. Don't forget that the aging is carried out in barrels at the distillery and not, for example, in the bottle after being shipped out. For Scotch whiskies the distilleries are in Scotland, so there was nothing stopping them carrying on producing and aging whisky as usual during the USA's prohibition.

Whisky for medical purposes was still produced and could be acquired with a prescription (and yes this was exploited) so aged liquors could have been provided for domestically reasonable fast after abolishment.

Its also worth pointing out that as the possession or consumption of alcohol was not prohibited by the law (selling and distribution was) people would have been able to stockpile it for personal use.

http://www.lawhiskeysociety.com/pages/Medicinal-Whiskey-Prohibition-Tasting