Best set on all machines the environment variable UEINIDIR to the directory on your portable HDD where the INI file and all other configuration files are stored. The HDD must have the same drive letter on all machines.
See alsoUedit32.ini in a different location than user or windowsBasic.mfg in another directory?How to transfer configuration settings to a new PC
Make sure that all additional files (Wordfile.txt, Htmltidy.cfg, Uetmplte.dat, Taglist.txt, ...) and all your macros are also on the portable HDD with the appropriate path and file specification in the INI.
There are only 2 files which are always in the application data directory of the current user: projects.lst and nfgroups.lst. I don't know if it is also possible to have these 2 files in a different directory. But you can forget these 2 files if you do not use projects. Well, I don't really know what these 2 files are for.