An aftermarket regular laptop AC power cord work with this Mini?

Their all the same. To be sold in the EU and America, they must all be certified the same way. No difference between one from Apple and one from a laptop charger. I had the problem when buying iPads with my dad for the family, we bought them in the US, but we needed European Adapters. We simply got a couple of the above mention cables and hooked them up - worked like a charm. Friend of mine lost his cable for his Mac Mini - I gave him one of the above mentioned and it worked.