A question we frequently get to hear is whether Hyper-V can run off a USB drive. In fact, there is a trick you can use to boot Hyper-V Server 2019 from USB, including older versions (2016, 2012).
In the article linked above there are instructions on how to set it up. A fast USB stick is recommended. We had good results with SanDisk Ultra using USB 3.0 and it’s also rather cheap.
Hope this helps!