Weapon traps can be more versatile than cagetraps, especially if you don't quite feel like lining the entryway 7 ways to sunday, since they auto-reset themselves. Cagetraps are oneshot wonders, in every way concievable. (But they can't spring on ginormous creatures, like FBs, unless the creature is unconcious or sufficiently stunned.) Weapon traps however, can, as far as I know. Just put the weapon traps in a rectangle around an indestructable artifact building, (like an artifact quern, or millstone), so that the FB focuses al its attention there, while the weapon trap relentlessly beats on it. I'd suggest using actually good weapons in such a trap though, since FBs tend to be rather... shall we say... "resistant".
Another option, is mechanism based droppable floor, with a hole in it for said artifact building to avoid being smashed out of existence. Lure the FB in, seal up the exits, drop the roof on it. Possible alteration, now that dropped items do damage, is to use a retracting bridge with dump zones on top, loaded with harvested clay boulders, or green glass blocks since those are infinite in supply. Just make sure that *all* routes into the fortress are sealable with BRIDGES, since floodgates and doors can be smashed by building destroyers, and the caverns often have flying beast people. The stories of angry caveswallow people are the things of legend.
This tactic also works good for taking care of gremlins, if you have them. They just love levers, so give them lots of random noble suicide levers in the caverns, and enjoy the spectacle.
[Just an aside, I remember reading a story about modding bugbats to be trainable as war animals, and how devistatingly horrible they were, since they were so tiny. It makes me wonder what putting [pet_exotic] and [trainable] on bees would be like.]