I will not answer how to do what your asking since thats adequately handled by other posts. Instead i am going to answer the concerns about the laser operation and engineering in general.
Dont get confused and too affected by the line width in illustrator. Its only meaningful in printing context. The laser and a human specification reader is only interested in the center of your line. There are several things going on that may or may not become a problem for you
You dont actually know the width of the laser line beforehand. I mean you could have a reasonable guess if the know the exact laser and its optics. But its not actually exactly known beforehand. A lot of things can change the day to day performance of the laser and material.
So you should have the shape overlap with the laser line. Because that indicates that you wish the engraving, print sillscreen etc. to reach the line. Not just outside of line. Not only does this apply to laser operation but also how engineers would reason about a specification.
Side note: unless your specification goes to a 5 axis laser. Its a bit of a question of how do you measure the width of the beam on the material. Do you measure exit width or entry width, average or something else?
The cut line may get offset by the laser operator to preserve the overall dimensions of your drawing. Again it is assumed that the shape is what your centerline does not width of stroke.
In this case the fill would need to hit center or even beyond. So just like in print production you probably want to have cut allowance so there should be a bleed over your line.