Depends to some degree on how that other voicemail connects to the system but you didn't say.
If is analog extensions, put then in a group, turn off the Message Button Goes to Visual Voice settings. Set the Voicemail Type to Group and set that group as the destination.
Otherwise, I would look at the 46xxsettings file the system is passing to the phones to see if the voicemail server address is somewhere in there (I know the conference server address is). If so, add a 46xxspecials.txt file with that address changed to whatever might work.
I say 'might' as its all guessing.
Stuck in a never ending cycle of file copying.