Inkscape - Exclusion/Difference: remove fill but preserve stroke (size)

Question

For my background, I'm not entirely comfortable with Inkscape, but I'm not entirely new with it either.

Say I have a large object with a smaller object inside of it. I want to remove the smaller object with Path -> Exclusion (or Difference). If I do this, the smaller object's fill will be removed and its stroke will be preserved. However, the stroke size will be reset. Is there a way for me to preserve the stroke size when using Exclusion?

Neither stroke to path or object to path do what I'd like.

Let me know if I need to explain myself more.

EDIT

I think I just figured it out. It looks how I want it to look at least. I chose the smaller object and selected Path -> Inset. Then I chose both objects and selected Path -> Exclusion.

EDIT

Nevermind, I didn't figure it out; it doesn't work for a different set of objects.

Here's the image. I'm trying to use Exclusion on the mouth and teeth.

Answer 1

As per your post I understood this way.

1. I created both the paths.

2. Duplicated the mouth path.Ensure that duplicated mouth path is in the top Z-order.

3. Select mouth & a tooth & apply path-difference. Now your result looks like this image. Similarly repeat step 2 & 3 for another tooth.

4. Now you can move the stroked teeth downward. You can now remove the stroke & fill the mouth area. The final result after these steps.

Is this the result what you want ?