Swap which characters share palette

There are two sets of character palettes. There's the character's battle palette, which is tied to the actor graphic and is located in a single list. This is very easy to change, since it's one table in one location. If your hack is compatible with FF3USME, you can just set this directly as the battle palette.

The field palette is more difficult. Field actors do not determine their palettes based on their character graphic. Instead, it is set in the event script via a command, which assigns a palette to an actor slot regardless of what their character graphic is. You'll need to use an event dump to see where these commands occur and change the destination palette to whichever palette you want. You have to find all the instances where the palette is assigned, because characters may be set up multiple times and their palettes will be changed by that event command running again.
The command in question is like this:

Code:

{43-0A-05}            Assign palette $05 to character $0A (MOG)

Now, that'll handle the player actors, but there's one other wrinkle with field palettes... when there's an NPC that's masquerading as the actor for a cutscene. For those, you'll have to adjust the NPC data to use a different palette value instead of what they're assigned to: that can be done with a level editor like FF6LE.

FF6Tools may be able to do all of these things, but as I am unfamiliar with that editor I can't walk you through how to go about it.