This is due to such information being store in the registry. One solution would be to use regedit to export the needed keys to the zip disk, then import them first on any new machine before you run mushclient. This is one of the problems that arises from the addition of the bloody registry, instead of the old method of storing things in a program specific .ini file in the executables own directory. If a program stores something it needs in the registry, it won't run on another machine very effectively (if at all).
The batch file would be something like:
regedit /E 1.reg "HKEY_CLASSES_ROOT\.MCL"
regedit /E 2.reg "HKEY_CLASSES_ROOT\CLSID\{11DFC5E6-AD6F-11D0-8EAE-00A0247B3BFD}"
regedit /E 3.reg "HKEY_CLASSES_ROOT\Interface\{11DFC5E8-AD6F-11D0-8EAE-00A0247B3BFD}"
regedit /E 4.reg "HKEY_CLASSES_ROOT\MUSHclient.TextDocument"
regedit /E 5.reg "HKEY_CLASSES_ROOT\MUSHclient.World"
regedit /E 6.reg "HKEY_CLASSES_ROOT\Typelib\{11DFC5E7-AD6F-11D0-8EAE-00A0247B3BFD}"
regedit /E 7.reg "HKEY_CLASSES_ROOT\Software\Gammon Software Solutions\MUSHclient"
regedit /E 8.reg "HKEY_LOCAL_MACHINE\.MCL"
regedit /E 9.reg "HKEY_LOCAL_MACHINE\Software\CLASSES\CLSID\{11DFC5E6-AD6F-11D0-8EAE-00A0247B3BFD}"
regedit /E 10.reg "HKEY_LOCAL_MACHINE\Software\CLASSES\Interface\{11DFC5E8-AD6F-11D0-8EAE-00A0247B3BFD}"
regedit /E 11.reg "HKEY_LOCAL_MACHINE\Software\CLASSES\MUSHclient.TextDocument"
regedit /E 12.reg "HKEY_LOCAL_MACHINE\Software\CLASSES\MUSHclient.World"
regedit /E 13.reg "HKEY_LOCAL_MACHINE\Software\CLASSES\Typelib\{11DFC5E7-AD6F-11D0-8EAE-00A0247B3BFD}"
regedit /E 14.reg "HKEY_USERS\DEFAULT\Software\Gammon Software Solutions\MUSHclient"
copy 1.reg+2.reg+3.reg+4.reg+5.reg temp.reg
copy temp.reg 6.reg+7.reg+8.reg+9.reg+10.reg temp.reg
copy temp.reg 11.reg+12.reg+13.reg+14.reg temp.txt
del *.reg
move temp.txt mush.reg
This should give you a copy of all the keys (that I could find) in a file called 'mush.reg'. You can then either right click on mush.reg and select 'merge' or use the command 'regedit mush.reg'. This should work on most machines, though I am not sure about ones that are set up to prevent you from installing programs and I only assume that the password is some place in that mess. The ones exported to 7.reg and 14.reg are probably not needed and it made no sense to export the one pointing to the uninstall, so I left that one out entirely.
I would prefer if everything not 100% needed in the registry got put some place else and that the ones you do need where autoadded by mushclient itself. It would make it a lot more usable for a number of people.