I'll do my best to describe it, but I'm a little tired.
The animations that Chrom has in Awakening and the cutscenes that display the battles of both Chrom and Lucina show the specific kinds of manuevers I mean. Because Lucina says that she learned her moves "from her Father," I think it's completely reasonable to incorporate her attacks into Chrom's moveset.
When looking at Chrom's in-battle animations, he jumps a lot (which isn't too uncommon for Fire Emblem Lords), and he angles his sword in arcs that look...very uncomfortable for his arm. Some of his battle animations seem to directly contradict what Marth does: For instance, when he rushes forward to strike, he stabs at an upward-diagonal angle, as opposed to Marth who slashes. When Chrom strikes upward, he slashes TOWARDS HIMSELF at an arc to essentially "uppercut" the opponent with his blade, and follow through outward to pull the opponent in.
When looking at the various cutscenes through Awakening, their are a lot of other moves that I find inspiring. One of the first we see is a fight against the Risen in the beginning. One of the small details that I find interesting in how he fights in this cutscene is how he uses two hands to strike with a forward slash for more power. Ike does something similar sometimes, but it's a bit more unusual with Chrom's smaller blade. In several cutscenes, when Chrom is able to use more power (such as when an enemy is being held off), he switches to a two-handed style that's much more straightforward than his regular way of fighting.
The most impressive display, though, is the cutscene of his fight against Lucina in Arena Ferox. Chrom's iconic pose comes from the way he (and Lucina) masterfully swings his sword around both of his arms in a pinwheel like pattern. Along with the two-handed fighting style, I think this shows that Chrom is fairly proficient in fighting with both of his arms, and makes use of switching arms (sometimes even throwing his blade) to get around his opponent. I think the most impressive manuevers in this fight are one in which Lucina combines a jumping roundhouse kick, followed by a sideways arced forward slash, and an incredible manuever performed by both Chrom and Lucina in which, from an aerial position, they rapidly front-flip while swinging they're blade toward the opponent. Stylistically, it DOES look similar to Ike's Aether in Brawl, but they are able to angle the attack in a way to launch themselves at their opponent.
Using these moves and animations as influences, I think Chrom can have an incredibly athletic fighting style that makes use approaching the opponent through leaping attacks/kicks and attacking by arcing his blade in unusual angles as he slashes, while being able to perform combos by rapidly swinging his blade as he switches hands, as well as more powerful moves where he uses both arms to slash in a forward arc (as opposed to a downward slam). Special moves can make use of the more "specified maneuvers" Chrom has displayed, such as the rapid front-flip spin and rapidly spinning the blade around both arms.
As for the Final Smash, I like the idea of making use of Fire Emblem Awakening's "Dual Support" system, where other characters jump in for team attacks. In this specific example, Lucina appears from a portal, and the duo perform a team attacks on the opponent; this example is entirely based on a cutscene early in the game.
I hope this was the kind of thing you were looking for. And thank you!