Thanks to all commenters, that video was very helpful in achieving my goal. The ideal thing, for anyone looking at this in the future please watch that video.
Essentially, from your modeling/rigging program of choice, you export the base mesh (your character, for example) and ANYTHING you want them to wear with the exact same skeleton, separately. Export character_mesh with character_skeleton, then export duster_mesh with character_skeleton too. You import your character_mesh to UE4 and leave the “Skeleton” tab empty so it uses the skeleton you exported it with (character_skeleton), then anything else needs to use the same skeleton upon import. Import Character, Character_Skeleton is made. Import Duster, use Character_Skeleton upon importing. Then when Duster is used as a component of Character, it can use the same Animation Blueprint.
I suggest saving/exporting a copy of your skeleton to import to any project you need to, so you can always have that exact skeleton for weight painting/etc.