I am looking for a minimalist Latex installation that can be installed on a USB key. I also want to use this key on my workstation without interfering with my installation (MikTex). What do you know?
Look at this description of making the TeXLive portable: https://tug.org/texlive/archive/portable-anchor.html
Running from USB
You can run the normal TeX Live installation and make the output directory be a USB stick. Then you do several things:
Use the tl-portable script to run completely from the stick, without touching the host system at all. As described in the documentation, tl-portable starts a new shell (command prompt) within which you do your work.
On the page https://tug.org/texlive/doc/texlive-en/texlive-en.html#x1-420004.2 we can read
4.2 Portable (USB) installations
The -portable installer option (or V command in the text installer or corresponding GUI option) creates a completely self-contained TeX Live installation under a common root and forgoes system integration. You can create such an installation directly on a USB stick, or copy it to a USB stick afterwards.