newbie question... camera suggestion

Hi everyone, I realise that I've ended up doing things a bit back to front here, but to spare you the long story I am looking to live stream an event in about a month's time. I have a good macbook pro with OBS (streaming works fine using image from my iphone running through OBS to restream.io

I have a BM Intensity Shuttle, which I originally bought thinking I could access a clean feed from my Micro 4/3 SLR (An old Panasonic Lumix G2) but it turned out that the G2 only put out HDMI in playback.

Before I stick the shuttle back on ebay, can anyone suggest a straightforward small camera that is known to work reliably into a shuttle on HDMI and thereafter into OBS. I'm looking to spend 2-300GBP max, really, but happy to go second hand if I need to.

It's going to be used every few weeks maybe to stream small rural concerts, so I don't need any bells and whistles and want to keep it simple, but unless you can advise otherwise I don't think a webcam is going to cut it.

Cheers!

Small and simple, the Micro Studio or Micro Cinema Cameras come to mind, can not get any smaller or simple to use, especially the Micro Studio which has a ready to use video signal, HDMI out will be HD only.
Both can do a clean feed on HDMI also.
Cheers

They do look perfect - not sure of the pricing in US but here they are coming in at 600GBP+ even second hand, over 1K new, which is way out of my budget at the moment :/

Is there anything more around the 200 mark that people know works well with the intensity shuttle? (not looking for a BM camera necessarily)

Thanks!