Half the point of the portable mode is not to touch the system configuration.
But you might try installing it as non-portable, then (with mIRC not running) move the stuff from %AppData%\mIRC\ to the folder in which you installed it, and change references in mIRC.ini that point to %AppData%\mIRC\ to point to the install folder. (Note that %AppData% refers to the Application Data folder under your user directory.)
This hack may not have the desired result—or even work at all; i've never tried it. But it's worth a shot, if you really want the peculiar config. (The alternative is to set up the protocol handler manually in the Windows registry—which i don't know how to do off the top of my head, and don't recommend to the average user, as you can seriously injure your system meddling about in there.)
Irgendwo über dem Regenbogen