Here's how I would do it. Certainly don't think of this as me trying to prescript your ideas in any way, I'm simply brainstorming how I would approach this if I were doing it. I know my tolerances for experimentation and homebrewing are pretty high.
General rules
Medium armor proficiency becomes Unarmored Defense. AC = 10 + Dex mod + other stat mod of player's choice.
Heavy armor proficiency becomes Unarmored Defense. AC = 12 + Str mod + other stat mod of player's choice.
Fisticuffs. Unarmed strikes are treated as a simple weapon, 1d4 bludgeoning, Light, Finesse.
Every class starts with simple Firearms proficiency by default.
Nonmagical Classes
Rogue. The default class for the setting, like Fighter in a normal D&D world.
Fighter. I'd probably use for soldiers/mercenaries. Allowed but not encouraged. Some subclasses might not work, determine case-by-case.
Barbarian. "Simmering violence in a cultured world" is a super fun trope to encourage for this kind of setting. Case-by-case for the subclasses, some would definitely need reskinning.
Monk. Maybe? I'd allow but definitely has to be the right concept. Lots of subclasses would need reskinning.
Savant. Int based nonmagical explorer and expert, fits right in.
Non-magical Ranger/Hunter. Tons of options around.
Magical Classes
Investigator. The "wizard" replacement, focuses on mysteries and rituals.
Warlock. The main source of hidden magical secrets.
Bard. Reskin as Psychic/Medium. Change casting stat to Wis, verbal components to nonverbal. Drop Song of Rest and Countercharm, possibly some ribbon to replace. Some subclasses may need to be reskinned. Might be too overly magical, I'm only about 70% confident on keeping this one.
Witch. The other "wizard/cleric/sorcerer" replacement. Reclusive arcanists, organized into covens/Hermetic houses/secret societies.