ok just to put a stop to this
NO INTERFERENCE ALLOWED
Shoot, even if he didn't have his shield the OP stated that weapons are the usual from under the ring. that means chairs are under there... and that's very close to a shield if you hold it right.. And with his strength he could Frisbee launch them with accuracy and speed!
The Recipe for Disaster asks for Blasphemy, but as for me, ask for me, I give it gravity.
Heh, that mirrors comic Batroc making the same assumption against comic Cap. That's a nice detail to add to the movie. Villains always seem to think Cap is helpless without the shield and they usually end up tasting a Cap special order knuckle sandwich before going night night.
Slight edge to Cap. Batman has the edge in standard equipment due to utility belt but Cap is not as nerfed without his shield. He's also slightly faster, stronger and more durable. Skill wise is probably a wash.