I would noe recomment to use the sketch that creates tour geometry as the source to create you laser cut pieces.
1. Greate a sketch to greate your 3D geometry. Thtis can be comprised of simple shapes and does not have to resemble the final outline of your design.
2. Add features eg. cutouts, lettering etc. perhaps with a number of additional sketches and extrude-cuts.
3. Once your 3D geometry is complete, create a sketch on top of the completed piece and project the outline of the 3D geometry into that sketch.
$. That finel, projected sketch you can export into a DXF file that can then be used to laser cut your design.
I've done this many times myself, so I know this is a solid workflow,
If this is not clear, post an image of what you are looking for and I can demonstrate it in a screencast.