16th century is poorly catered with plastics, especially the later half.
Warlord does three plastic sets of landsknechts, but these tend to be rather aimed at 1520's or so.
Wargames Atlantic makes the two conquistador sets (infantry and cavalry). They also have a "renaissance heavy cavalry" set, that would be best suitable from mid-16th century onwards, but is certainly not anywhere close to civilian style.
Even with metals, the later 16th century is poorly catered for, though The Assault Group has some ranges for the period. Would these look like what you are searching for:
https://theassaultgroup.co.uk/product/sea-beggar-captains-command-group/