Configure Chrome or Firefox to have an "open link in default browser" action
Create a browser extension that uses Native Messaging to execute open url on the command line when you right-click a link.
This is all I could think of. I wanted this too so I built it for Chrome.
On Windows 10 with Chrome, I have found that opening a link in an incognito window will open a link in a new incognito window if none existed, or open a link in a new tab in an incognito window that does exist.