Two ideas: a) try a gradient fill instead, or b) clone the object, and apply the fill to one object and the stroke to the other. Later, you could group the two objects or define the whole thing as a symbol, allowing you to treat it as a single unit.
Actually, you can control the stacking order of filter effects. So you could apply the Inner Shadow effect to the object without the stroke, and then add the Stroke via the Photoshop Live Effects (at the bottom of the Filters menu).
Both this and the Gradient Fill options would allow you to save the appearance as a Style, where it could then be applied to other buttons or objects.
I think solution a won't work, because the light inner shadow-like yellow is also visible on the inner right and left edges of the button. Solution b works, but ideally I was looking for a solution with only one object.
Before you give up on the Gradient Fill approach, be sure to try different styles—like Contour, for instance—and realize that you can scale the gradient and reposition it, to get the right effect.
Also, did you try the third solution: applying both Inner Shadow and Stroke as filter effects?