Do they need a trash counter? Champions don't, and Hand Cannoneers have half the hp, over double the gold cost, and unless you're Turks you can only begin massing them several minutes into Imp, since Chemistry is such a slow research. Even without bonus damage you could probably still overwhelm them with skirms, especially with micro given the accuracy issues.
Champions sole purpose is to counter trash and it still has an anti infantry weakness. They also don't get any range like hand cannoneers. Every civ has access to skirms, and not every civ has access to champions or heavy cav archers with thumb ring.
So yes. Hand cannoneers do need a weakness and I'm fine with elite skirm being said weakness.