Can I import an object that is influenced by bones, without its bones?

I'm working on a character customization project. The character has some animations, so its objects, like shirts and pants, suffer influence from its bones. I'm using Blender to model and animate and exporting it as a fbx file.

What I've been doing so far is importing the whole character with all objects attached, and working on the customization by enabling and disabling the GameObjects.

It got a little out of hand working that way, because it implies that every time I have to add or edit one object, I have to re-import the whole character, and set it all up once again.

I'm looking for a way to import a single object, let's say a shirt for example. How can I make it work with the animation just by dropping it into the character hierarchy?

I noticed that all objects that work with the animation have a Skinned Mesh Renderer component, but if I import another object, it comes with a Mesh Renderer instead.

Any tips on how to accomplish this?