You can place install-unity on your portable drive and run it on any Windows or macOS machine. It will handle downloading and installing the Editor to your desired location, which could also be on the portable drive.
Unity relies on Microsoft Visual C++ Redistributables. If the guest computer is missing these, Unity will fail to launch. Keep a copy of the vc_redist.x64.exe installer in a Prerequisites folder on your USB drive so you can install it quickly if a guest machine throws an error. unity portable install top
I can provide the exact scripts and folder trees tailored to your target setup. Share public link You can place install-unity on your portable drive
Go to the official Unity Download Archive web page. unity portable install top