UFT will run on Windows ME, at least version 3.1 does. I've been running Windows ME for a few months now. Although I have switched to TMG I occassionally go back to UFT to see how they did something and while I have not done any large amount of processing (I have ran some reports) all seems to be working. I would install UFT on your new computer with Windows ME and transfer you files to it using the UFT backup/restore procedures.
Like Myrnice stated, TMG will read your UFT files and transfer almost everything via their GenBridge procedure so you don't have to reenter everything. If will even import from your UFT backup files.