Ok, well I would say hand drawn paths are almost always better. But if the double lines are ok, and especially if they are needed, then Trace Bitmap is a good solution.
To be honest, this is a point I'm a little confused about with some of the CNC type projects. And the person who designed most of those extensions doesn't participate otherwise in the community, so you have to go to his (Russian) forum to get help. I've even posted there, offering to write tutorials, if someone would explain it all to me. No replies. So I don't know, does the machine need 2 paths to cut out wood between them? Or can the machine make a specifically wider or narrower cut along a single path? And then when we try to help people with their projects, they rarely come back and tell us the result. So we can't make use of their experience. It's an unfortunate "no-man's land" sometimes, using those extensions.
Anyway, I find that almost every time I use Trace Bitmap, I do a lot of trial and error, to find the best result. From my experience, I would say all the defaults should give an acceptable result.
Mode tab > Single Scan
-- Brightness Cutoff 0.450
If you want to try for more precision, there are also some options on the Options tab, which can help. But for some reason, those options aren't updated in the Preview. I've actually submitted a feature request to have them included in the preview. Anyway, that's why I say trial and error will probably be needed. Plus that preview is tiny....although I haven't used it for a while, maybe the preview is larger now?
Options tab
-- Supress speckles (if it's a very clean image, not photocopied or otherwise scanned in - this can be ignored - otherwise, it can help to clean up images which may have been scanned in)
-- Smooth corners (in my experience, I would say this needs to be a low value. Otherwise those points on the flower-like design might get rounded)
-- Optimize Paths (I would say give this a high value, but again, you can experiment to see what works best)
In case you've never used Trace Bitmap yet -- the trace result comes out right on top of the oringinal, and often it looks like nothing has happened. This is one of the many times when the status bar is so helpful. It tells you what kind of object is selected. So if, after the trace, it says "Path....." that's the result. If it still says "Image...." it's not finished yet. After it's finished, you can drag the new paths away from the PNG.