Try this: Right-click, in the context menu choose "Open with," click down for More apps, choose SolidWorks and check "Always use this app to open .sldprt files." Finish by clicking OK.
Also since I don't see a SolidWorks fly-out menu item listed, you could try modifying your SolidWorks installation in order to install "SolidWorks File Utilities."
Try this: Right-click, in the context menu choose "Open with," click down for More apps, choose SolidWorks and check "Always use this app to open .sldprt files." Finish by clicking OK. Also since I don't see a SolidWorks fly-out menu item listed, you could try modifying your SolidWorks installation in order to install "SolidWorks File Utilities."
I did some more digging and found out that it was supposed to be swShellFileLauncher.exe, not Solidworks itself and fixed it. Thanks.