The Blackmagic Micro Studio camera is definitely a good option to consider. It's also one of the only small cameras you are likely to find with 4K output over SDI and it has interchangeable lenses so it's easier to get the angle of view you want.
But this also means that depending on what lens you attach the Micro Studio camera, you may end up with a package that's quite a bit larger than an action camera or one of the Marshall POV cameras (even with one of the Micro 4/3 pancake lenses attached, the Micro Studio Camera is still well beyond a GoPro in size).
So if you need something smaller (action camera sized), you might check out one of the following:
- Sony FDR-X3000
- GoPro HERO 5
- Garmin VIRB Ultra 30
I believe these cameras are capable of 2160p2997 live output over a Micro HDMI port.
Many of the other 4K action cameras either are not capable of 4K output over HDMI (GoPro Hero4), are not capable of any live HDMI video output (Nikon KeyMission, Olympus Tough TG-Tracker), or lack an HDMI port entirely (Yi 4K and 4K+). And unfortunately Marshall doesn't make any 4K capable POV cameras that I am aware of.
Using a Teranex Mini to upscale 1080p video is also a viable option in many cases. Depending on how far you are from the screen, and what content you are shooting, it can often be hard to differentiate 1080p from 2160p even when shooting with high end cameras. Not to mention that most viewers will probably be watching in 1080p or below anyway.
And even if watching on a 4K screen, few people are likely to notice the resolution difference when cutting between an small POV camera in HD and a full-sized camera in UHD. The POV camera would probably look different, but that has much more to do with color, dynamic range, depth of field, lens quality, etc. than it does with resolution. You could cut between a 4K action camera and a full-sized HD camera and the full-sized camera would still look better in most cases.
Keep in mind that only the Teranex Mini HDMI to SDI model does upscaling to UHD, and it does not do any frame rate conversion. So if you want 2160p2997 output you would need to feed the Teranex Mini a 1080p2997 input over HDMI. If you need frame rate and resolution conversion, you'd likely need a Teranex Express.