The recent files list is stored within blenders config directory. Blender searches three places to find it's config files, referred to as the local, user and system locations, see this page for platform specific variations. The first place searched is a local config folder that is in the same location as the datafiles installed with blender.
One way would be to keep two copies of blender, and create a local config folder for the 'SE' copy so that when you run the 'SE' copy you get a unique config which includes it's own recent files list.
You can also adjust the locations that are searched by setting the environment variable
BLENDER_USER_CONFIG. The available environment variables can be listed by running
blender --help in a terminal.
$BLENDER_USER_CONFIG Directory for user configuration files.
$BLENDER_USER_SCRIPTS Directory for user scripts.
$BLENDER_SYSTEM_SCRIPTS Directory for system wide scripts.
$BLENDER_USER_DATAFILES Directory for user data files (icons, translations, ..).
$BLENDER_SYSTEM_DATAFILES Directory for system wide data files.
$BLENDER_SYSTEM_PYTHON Directory for system python libraries.
$TMP or $TMPDIR Store temporary files here.
$SDL_AUDIODRIVER LibSDL audio driver - alsa, esd, dma.
$PYTHONHOME Path to the python directory, eg. /usr/lib/python.
On a *nix system you can create a shell script called
blender-se which sets this location before starting blender.
Then when you call blender normally the normal config files will be used. On windows a similar .bat file could be used.