I believe zornhut is held with the sword on the shoulder. The text makes this clear - of the zornhut, Meyer writes: "Stehe mit deinem Lincken fuß vor / halt dein Schwerdt auff der rechten Achsel" which I translate as "Stand with the left foot forward / hold the sword upon the right shoulder" (auff/auf causes confusion for English speakers who think it means "off" but it is actually a preposition which implies "on" or "upon" something (i.e. with contact) rather than off and not touching. Anyway, zornhut (or the earlier vom tag) with the sword upon the shoulder is not lazy - it's very powerful.
--I've always seen Zornhut as kind of a "wind up" position to prepare for a powerful strike. When you see illustrations of it the weight is on the rear leg and the torso actually twisted to the rear. The sword is not only on the shoulder, but the blade trails behind the back as well. That's not the same thing as just resting the sword on the shoulder because you don't want to hold it up in the air. But regardless...Meyer does not describe a zornhut with the sidesword, although he does say that everything he's talked about before can apply....so by extension you could include it. But I think it would be a risky thing to do in front of an opponent carrying a long thrusty-type weapon.

