There are no supported Mini-PCIe video capture cards. I have not seen anyone try to use one. I highly recommend giving it a shot. Others have been trying to use a Mini-PCIe graphics card. Take a look at this post: https://communities.intel.com/message/225078#225078 it’s not the same but the process of installing the drivers should be about the same. I would also recommend looking though older post for additional information.
You can take a look at this post: https://communities.intel.com/thread/48380 . That might give you an idea on what considerations you should have for your project, you can give it a try then post your results I know they are going to be useful to other users.