Dedicated streaming devices will not have the ability to switch between camera sources, you’ll need live encoding software running on a computer for that. I don’t think I’ve seen any dedicated streaming devices that work with USB webcams anyway, they seem to only accept HDMI, component video, or composite video connections.
If the cameras are USB-based you may also run into USB bandwidth issues with too many cameras connected to a single machine. Top speed of USB 2.0 is 480Mbps but in practice this threshold is much lower and these webcams are transmitting uncompressed video. I’ve seen USB bandwidth issues occur with just two or three webcams, four would almost certainly be problematic unless the laptop had separate dedicated USB buses by some chance.
Capturing multiple HDMI sources at the same time can also be problematic and you would need desktop with a capturing card for each HDMI camera, the card would also have to be compatible with your live encoding software.
You could probably get away with having a single HDMI camera and two USB webcams, using an external HDMI capturing device that works over USB 3.0 or Thunderbolt.
Finally you could always use a mechanical HDMI switch to switch between multiple HDMI sources with only using a single HDMI capturing device. It’s a low tech solution and you wouldn’t be able to preview the video before you switched it over like you could in live encoding software but it would “work”.
Also, I’m assuming you mean SD cards not SIM cards.