My proposition for a new, non-swordsman Fire Emblem fighter is the Fell Dragon, Grima. And I don't mean Grima in Robin's body; I'm talking about Grima himself, wings, fangs, shocking human face and all.
~What kind of attacks could he use?
Looking at his full design, Grima could possibly be a lethal attacker on all fronts; jabs using the horns on his head, his multiple pairs of wings, and his unique breath weapon Expiration could be a major factor in smash attacks or special moves. Being the main progenitor of the Risen, he could also use them to his advantage, calling upon randomized classes that appear for somewhere along the lines of five seconds and doing something to help Grima (i.e. a priest or sage heals him, berserkers go after who's first, et cetera).
~Isn't he, like, the size of multiple football fields?
Yes, in Awakening at least. However, he does make another appearance earlier in the Fire Emblem timeline; in Shadows of Valentia, Grima appears as the final opponent in the Thabes labyrinth accessed upon clearing the game, where he is simply known as "the Creation," and poses as the ultimate challenge for Alm & Celica. There, he's still large, just nowhere near the titan he grows up to be in the Awakening era. Plus, lore dictates that he was actually born around the size of a thumbtack, and continued to grow in size as time went on. Grima's size in this game could be downsized in a similar vein to Ridley, and even then, he could potentially be the largest character in the entire game, even moreso than the Space Pirate.
Sorry, Rids.
~What about a Final Smash?
For Grima's Final Smash, it could potentially be a cinematic where opponents are taken to an area where they're confronted by the vastly bigger Awakening incarnation, who then proceeds to unleash his own take on Expiration. The damage would be massive, and could possibly be an instant KO if percentage is high enough.