Viola would either go for the rapier or the estoc, the two weapons associated with aristocracy, Argent however would aim for the broadsword or the scimitar, the weapons that seem as if they've seen battle, he'd appreciate that, they would then discuss it, Argent, being who he is, would decide to compromise, and they'd go with the estoc, as the more militaristic of the two blades that Viola would want to use, which would appeal to Argent as well
that's just how I see it anyway