And if you wanna save some cash, any $20-25 hdmi to usb capture card will work just fine. It won't give you uncompressed video, but you won't need it for this use case.
I've been bitten in my ass lots of times by these things. Random crashes, overheating, dodgy connectors that don't tolerate even the slightest movement... thanks but no thanks, the cheapest DeckLink clocks in at 150$. Downside is you'll also need a Thunderbolt PCIe case, but eh. It Just Works (tm).
And if you wanna save some cash, any $20-25 hdmi to usb capture card will work just fine. It won't give you uncompressed video, but you won't need it for this use case.