Possible to Stroke only outside of illustration?

I have the following illustration:

I want to try just putting a small stroke that goes around the outside of the drawing, however when I do select all and apply the stroke, it obviously strokes the inner parts of the drawing (for instance the mouth, eyes, dimples, etc). I've tried merging all of the layers, but it doesn't work. Does anyone know how to do this or is it even possible? Thanks.

KiSS