IF the old disk is still bootable, just boot to it and run what you need. Press the F-key that corresponds to 'boot options' or 'select boot drive' and then pick the HDD.
But to answer your question, if th old hdd is still bootabel then yes a migrate os program would still be able to work. I would suggest you backup the hdd first.
It would probably be quicker and cleaner to just reinstall word & Excel, all your data files on the hdd would be fine & still work fine if you did that.