Doing this workflow in Alias there is a fit curve tool which allows you to rebuild curves using the exact tolerance or curve parameters. For almost any type of Illustrator artwork I will normally do that because even very simple geometry (The Circle in our old logo) would sometimes come across with bugs/quirks.
Rebuilding the clean geometry gives you more precise control which will ultimately let you get exactly the end result you want. I’m not sure if Solidworks has any features for reducing curve complexity within a sketch, but that could be another good place to start.
It could also be worth checking your construction/geometry tolerances. If your construction settings are too loose or tight that could cause issues during export.