I believe USB to HDMI cables are only for output and your Inogeni is what you want to convert video signal to a datastream your encoder will recognize. I use the Blackmagic miniRecorders for the same purpose. Make sure using USB3 if doing over 1080 resolution. Not a fan of using client PC. Just make sure it’s fast, all background software if off and no screensavers. Also suggest doing location speed tests (and actual video tests) to confirm you have a dedicated (unshared with anyone else) 1.5-2Mbps for HD, 5Mbps uplink for 4K. Become friends with their (or venue) IT people. Use high quality cables everywhere – HDMI, USB, ethernet – and take backups; and backups to backups is a good idea.
Have fun!
Steve

