Hyperdeck should work.
Inputs can be HDSDI, HDMI, and others.
It’ll record to uncompressed / prores (any flavour) or DNX quicktimes. As long as your edit program can work with one of those, you should be good.
Use a dock, mount your SSD in your edit bay and copy the file across. Only catch is the files are originally saved as “capture001” “Capture002” etc. you can’t name them anything specific until you access the ssd through a computer.
Glenn