mr_eight

you didn’t specify which camera you use, but here’s a cage for Sony:
https://www.bhphotovideo.com/c/product/1449314-REG/smallrig_2238_arca_qr_half_cage.html

Yep.
 
Again, you don't necessarily need a separate clamp -- you could just bolt an L-bracket directly to the cage.  Of course, using Arca-Swiss clamps or other quick-release system makes the changeovers faster (and adds height to the camera).

I think most L-Brackets take 1/4-20 threads on both sides, so you might not even need a separate mounting clamp -- Arca-Swiss or otherwise.

@tupp thanks for dropping a reply. I appreciate it and confirms my thoughts as well. I might as well take the plunge and find out.  Makes sense to have a camera with an arca L-Bracket incase there is a need to shoot vertical videos. 

@kye 
Thanks for your feedback. I was looking at the height dimensions as well and might need to see how well a medium sized cage fares including in portrait orientation as well. 
 I have heard about Peak Design having a very low profile but need to check it out in person now that I have your feedback. 
@tupp
see attached screenshot taken from Wooden Camera's instruction booklet, so it should be possible to mount a arca-swiss clamp
 

I haven't done that specifically, but the concept is sound.
The challenge in your situation would be ensuring that there's enough clearance for the QR plate (both female and male) and the camera to fit under the top part of the camera rig.
I've invested a bit into QR plates and mounts to make my equipment interchangeable depending on what I'm doing.   I have a tripod, monopod, Gorillapod 5K, Manfrotto Pocket and a Peak Design Capture, which are either designed to receive QR plates or I've added them.  Then I have my GH5 and Sony X3000 action camera with QR plates from Peak Design on them, so either camera works with any mount.
The QR plates from Peak Design are the best I've found as they're well made and are super-small and low profile.   I've even put a wrist strap on the one on my GH5 for when I'm hand-holding it (which is common for me) and the strap doesn't stop it being mounted in a QR mount.  

Not familiar with the Wooden Camera cage, but most Arca-Swiss clamps have standard 1/4" or 3/8" female threads or have a counter-sunk hole.  So, if the cage has a way to attach cameras/plates with those threads/hole, then it should be easy to find an Arca-Swiss clamp that works

A couple of my local camera shops are clearing out their Wooden Camera demo units and I want to pick one of these up. However, my issue is that I primarily work as a photographer and use the same body for video work.
My video work is in the early stages and I spend about 1-2 hours a week shooting, mainly documentation work on construction sites. 
I saw Gerald Undone talk about the small rig's QR cage,  and I like the quick release built into the cage body.  I haven't pursued SmallRig due to delivery from China and with covid,  I don;'t know how long it will take to get to me.
I'm throwing it out there to see if anyone has attempted to add an arca swiss clamp to the Wooden Camera Unified Body's base where normally the camera's bottom goes? Or if anyone know that is even possible? 

Due to the weird state the SSD gets into when being read on the MacOS which causes DiskUtil to fail upon erasing the SSD. I dont know what I did but I managed to reformat the SSD to exfat. Plugged it into the Ninja V and viola it works!!! 
Even got the firmware updated but I noticed skippy the kangaroo appearing on the recorder on a few occasions. Just  maybe I need a new SSD. For now it will suffice since I am just shooting random things at home and trying to get familiar with the whole new set up.
Now to decide on what SSD to get next!