I never really specified handedness in my characters either, but I guess it's something to think about.
Smokey's almost definitely right-handed, though I'd argue it doesn't really matter much in his case. Matchstick isn't exactly a precision weapon, and his simple fighting style doesn't require any excessive amounts of finesse, so he could probably get away with switching hands on the fly pretty easily.
Aurelia's also right-handed, and she's probably my only character where it really matters, as she uses both sword and shield. Although, if she's on her unicorn, and I'm pretty sure she can overcome any disadvantage a southpaw would present with Noble Steed's raw power.
Toast is an acrobatic freak of nature who grew up in a circus as an only child with a lot of time on his hands. Also, his father and mother were an acrobat and a magician, respectively. Naturally, he learned to be ambidextrous, as evidenced by his dual-wielding fighting style. In fact, in one iteration, he had a third sword that he'd juggle with in combat, but I ultimately scrapped that idea because there were too many ways for that to bite him in the ass.
Lucas, as the closest thing to a self-insert I'll ever do, is left-handed. However, also like me, his dominant eye is his right eye, and thus shoots from his right side. In fact, his handedness hardly comes into combat at all, since the only thing he'd do in melee is try to clock his opponent in the face with his lantern or blast them back with dust.
It also doesn't really matter for Clara, either, as she also doesn't really do melee combat. So I flipped a coin, and I arbitrarily decided she's also left-handed. Who knows, maybe I'll give her some melee options after she's been through a few threads.