Electus Matari is the Shield.
Any swords that need a wielder?
You definitely have it right that we in EM do not really actively hunt targets outside of the Republic, and when we do something to assist the militia it's more in the interest of retaking Matari systems rather than pushing to take Amarr systems, but you may have a limited view on how defensive vs. offensive our activities are.
Speaking as a 3rd shift FC (01:00-06:00), and as a solo-hunter, my fleets do alot more hunting for targets to gank mercilessly, and not a terrible lot of defending systems that are distressed. I take great pleasure in baiting and then out-blobbing blobbers, and I usually have to use neutral bait in any area we've been working in alot, as EM bait just isn't as tempting after awhile.
In truth an EM fleet is more likely to be hunting pirates than Amarr, but that doesn't mean most of us wouldn't drop whatever we are doing to chase of a FW mission runner or plexer whenever we spot them, or at the very least let someone know that can chase them off.
Also, when we do war-dec a pirate corp or alliance and they set-up missioning or mining bases outside of the Republic...we do trace and hunt them wherever they go.
I don't think it's unfair to attribute a good bit of the sword as well as the shield to EM, so what did you have in mind exactly?