To save some computer resources, I would go with an external capture device. Essentially, a pass thru capture device (push a button, it records to a thumb drive) and your output gets passed through to the projector/monitor, etc.
I’ve had great luck with the HDML Cloner Alliance H.264 capture devices or you could go with something more professional that will record 4:2:2 or 4:4:4 4K/60fps.
The downside to the professional solution is price and storage. These files get big fast and most will be ProRes. Atomos, BlackMagic,–and some others make portable monitors with built-in recording capabilities. They usually start at the $300+ range.
The benefit to the cheaper standalone capture devices has to deal with file size, unit price point, and my favorite, HDCP capture. I’ve been at conferences where the BlackMagic system wouldn’t take in the input of an iMac because of an HDCP issue. Just looping it through one of these devices can break that.
Looks like there is a 4K/30fps H.265 capture solution from Cloner Alliance now.https://www.amazon.com/dp/B087TM4YRN
You can get the same box from a competitor for less, but at least with Cloner Alliance and Amazon, you can send it back if something is wrong. If you don’t need 4K/30 capture and only need 1080p, you can save about $100 buying one of their other boxes.
Most of these devices have a USB computer capture option, but there’s latency sending it to the computer.
Something of note: The UVC (USB Capture) devices such as Magewell, iEi, and so on require some CPU power. If your computer is older or limited in resources, this might cause more latency in the capture.