How to set up the system so that when I click a link in any (non-browser) app it opens in Firefox in private browsing mode?

I'm using macOS Sequoia. My default browser is Firefox, so whenever I click a link in a (non-browser) app it opens it in Firefox. However, it opens it in a 'normal' browsing window, and I'd like it to open in a _private_ browsing window. I tried to search the net, but have only managed to come up with results for Windows. Those results mentioned changing the properties of the shortcut used to open Firefox and adding the -private-window command-line argument. I thought it made sense and might work on macOS too, but there seems to be no 'shortcut': all I can find is that in the System Settings I can choose the default browser, from a closed list of browsers installed on my system, with no option of any customisation (not even the option to choose a different app, let alone specify properties and/or command-line arguments). Clarification: I'm not interested in disabling 'normal' browsing altogether (I've found an option in Firefox to make it always private, but that's not what I want – I do want to allow 'normal' browsing, I just want external links to open in private browsing mode by default). Any help would be much appreciated!