It doesn't matter what your installed Tixati does and where it is with portable mode. Portable mode saves all settings in its own folder and registers/unregisters .torrent and magnet-link file open associations on startup (and you can set to revert it on exit). Once you've done it: you'll only start the "portable mode" .exe file.
One more thing: don't forget to move the incomplete pieces folder if you wish.
Here's a directory listing for portable mode (all the files it needs must be present in the same folder as .exe)
downloads/ (well this is just the default setting)
Note I've excluded "lastloadok" files
Step 1: you don't need to redownload Tixati, just create an empty file "tixati_portable_mode.txt" where you want to have its data
Step 2: Move .exe to that folder
Step 3: Move dat files there
You can test it now with any folder and it will continue where it left off. Once you have the HDD, move this new Tixati folder there and then start managing file locations
PS: The big USB3 HDDs by WD/Seagate are the same as internal HDDs but cheaper. The WD HDDs specifically are the rebranded server HDDs on helium. You can extract them from their enclosure "shucking" and use them normally in your PC (you may need to cover (isolate) the 3.3V pin physically on the SATA power connector as it controls power up/down and defaults to down)