Not really the easy way, but this is how you can make your wine application show up in Preferred Applications.

You probably don’t have a .desktop file for you wine app. Go to /usr/share/application and find one entry that also shows up in your Preferred Applications->PDF list. Open that entry with a text editor: that’s how your new entry should look like (I recommend looking at /usr/share/applications/xreader.desktop in particular). You must have the MimeType field for Preferred Applications

Create your new pdfxchange.desktop file and place it into ~/.local/share/applications so it will be picked up by the OS and it should show up in your Preferred Applications list.

The only thing you need to figure out yourself how to make pdfxchange open a file from the command line, you need to put that into the Exec= field.

For you it might be something like this: Exec=env WINEPREFIX="YOUR_PDFEXCHANGE_WINE_PREFIX" wine "YOUR_PDFEXCHANGE_WINE_PREFIX/drive_c/path/to/pdfxchange.exe" Z:%f

Try it in the terminal (without Exec=) until it works. %f is the file you want to open.

If there is a good PDF editor that is Linux native let me know

You and me both, I don’t have a great solution for that yet. I’ve used Foxit for Linux before with decent results, but it doesn’t have full editing capabilities.

This ubuntu forum conversation had several recommendations, including PDF Master if you’re willing to pay for it. (The free version has watermarks.)

PDF is such a standard format now, I feel like there should be a better open-source PDF editor.