TLDR, scroll down to the script. Make a .sh file, allow it to run as a program, set it as your default program to open whatever filetype

Navigate to the appropriate/your favorite folder to store portable applications. Make the below script as a new file called WhateverYouWant.sh
Fellow newbies, the .sh is important.
Then set this .sh file’s permissions to allow executing this file as a Program; may differ by distro.

#!/bin/bash

# Script to set a windows application (that runs through WINE) as the default to open PDF files:

# PURPOSE: To convert Linux-style filename to Windows-style
# to pass as an argument to wine when starting PDF XChange Viewer
Filename="z:"${1//\//\\}

# Assuming you use the default installation folder for PDF
# XChange Viewer in Wine
App='eval wine "C:\Program Files\Filepath\To\Your\PDFXEdit.exe" "'$Filename'"'
$App

# Adapted originally from:
# http://sodeve.net/foxit-reader-on-ubuntu-linux-through-wine/
# Archive.org'd at: \https://web.archive.org/web/20160918205551/http://sodeve.net/2007/12/foxit-reader-on-ubuntu-linux-through-wine/
# Additional credit in 2024:
# https://forums.linuxmint.com/viewtopic.php?t=153092
# https://web.archive.org/web/20150213210206/http://crunchbang.org/forums/viewtopic.php?pid=173574#p173574
# https://web.archive.org/web/20150213210203/http://www.fsavard.com/flow/2009/03/pdf-annotation-under-linux-with-wine-and-pdf-xchange-viewer/

You can also check the appropriate windows-formatted filepath with Winetricks, using its built in windows File Explorer, finding your .exe, and copying the path starting from "C:".
[Edit: the default install folder in the script would normally be C:\Program Files, my bad. I downloaded the portable version and shoved it wherever, so my filepath looks like “C:\users\Froggy\Documents\PDFXchange test01\PDFXEdit.exe”]

Mint Cinnamon 21:

• right click your shell script file, Properties > Permissions > check on “Allow executing file as program”.
• Then find a PDF file (or whatever filetype), right click, Open With > ‘Other Application…’ > browse for this .sh file you just made.
• After selecting this .sh file, be sure to select “Set as default” before clicking OK.

I could not tell you for the life of me why this didn’t work with a .desktop file on Mint 21.

I spent the past few hours down the wrong rabbit holes with .desktop and exec=wine ‘filepaths’ and just about died of asphyxiation from absolutely nothing happening. I’ve been wanting to do the same thing too for a while, but decided that right before bedtime was the perfect time to look it up.
[Edit: I figured out spacing in the script. Also moved the Mint specific instructions down the comment for flow clarity]

If you click with right button over a PDF, select “open with…” doesn’t it show an option to select default app?

I don’t know cinnamon very well, but I think this is possible

For PDFEditor, the best option is OnlyOffice, not libreoffice. You can download an appimage on their website to test that out.

Also, for CAD, consider giving QCAD a go (if it’s 2D cad/cam you’re after). If it’s 3D cad, consider the free version of OndSel, a more sane version of Freecad.

LibreOffice Draw can edit PDFs. For just a pdf reader, I use Zathura, though it may not be for you since it’s very keyboard-based so might be confusing to someone coming from Windows. I think Cinnamon must come with a default pdf reader right?

Is there any way too edit file associations in settings? I know you can in plasma but idk about mint.