Driven, you have the right idea. There is no need to redraw.
Download the free and fully-operational 14-day trial version of ViaCAD 2D/3D from Punch! software. Here is a current link...
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ViaCAD 2D/3D can 'import' native Sketchup V7 files and many others including (but not limited to) file types that are important to us like STL, STEP, and DWG/DXF!
So please note...if you are using SU V8 or higher, (until ViaCAD updates their software) you will need to do a SaveAs V7 on your model first or ViaCAD will not import the file. ViaCAD does not warn you when you try to open SU V8. Basically, nothing appears on the screen and there are no failure notices. So make sure you SAVEAS V7 first. SU free version allows you to SaveAs all of its older file formats.
Make sure you check the 'Facets to NURBs' checkbox of the SU import dialog.
Once your model is in ViaCAD 2D/3D, choose Export from the File menu, then choose from the wide variety of file formats, including ACIS (SAT), Adobe Illustrator, BMP, CGM, DWG/DXF, EPS, Facet, FACT, IGES, JPG, RAW, STEP, STL, Text, Viewpoint Media, FRML, and Wavefront OBJ. I only tested a couple of these.
My only minor complaint is that ViaCAD software does not provide any sort of clue when an export process fails. A log file would have saved me some time in determining problems with my SU models.
Basically, this is a fantastic piece of CAD software and the $99 price is well-worth it if you need to export your SU files to a solid-model file type like I did. MAC users can rejoice also as they have a MAC version as well.
ViaCAD appeares to be a highly capable 2D and 3D package for those looking for something affordable. I hope to dig into it more over time. It appears to be well-conceived and even has the push-pull method for shape manipulation that Sketchup help make famous.
Have fun.
Steve