I've tried it properly this time, with RegisterFirefoxPortable and all the stuff, and got 2 issues:
When the browser_launcher is pinned to taskbar (by drag'n'dropping the browser_launcher or its shortcut) and is launched from there, Opera/Vivaldi are opened in a new taskbar "toast", instead of the place of the pinned launcher. In other words I get pinned icon in one place, and the opened browser in the end of the taskbar.
I had to fix it by pinning the opened browsers (via taskbar), which resulted in the original browser executables being pinned, and then manually modifying each pinned shortcut so that they point to browser_launcher. So far it works, hope they will not disappear from the taskbar after reboot (sometimes it happens when the pinned shortcut was modified).
When browser_launcher is registered as a default program with RegisterFirefoxPortable and the .reg fix, it doesn't appear in "Default Programs" in control panel. Have no idea why...
I have checked the registry and saw that RegisterFirefoxPortable did its job like it supposed to, so it is not this part that fails.
I would assume that the original launcher has some sort of signature or something, "Default Programs" checks each registered default program if it is signed or not (while fetching the list of programs), and hides those that are not signed.
I got it work by renaming browser_launcher.exe to whatever, renaming the original launcher to browser_launcher.exe, doing the RegisterFirefoxPortable procedure, and then renaming the launchers back. After that the browser entry is still in "Default Programs", opening web-files launches browser_launcher.exe, and the browser runs with all the arguments.
After getting these two fixed, the launcher works great so far, I'm now using it with Opera and Vivaldi (both are standalone/portable).
Did you have these issues?