The cheap video switchbox things are NOT a good choice for the task at hand – they simply change the connection from one set of inputs to another, breaking the signal momentarily (think of physically moving the cables yourself super fast!). The two or more inputs are not synced and there is a glitch or signal break when switching that would most likely cause the encoder to stop dead in its tracks. Those boxes are meant to switch between the game console, VCR, and DVD player, that's it.
Real video switchers use some internal method of syncing up the two or more video input signals so that switches are seamless and do not interrupt the video output signal at all.
Some streaming software apps will allow switching in the software itself, but this assumes Firewire or USB cameras usually (digital). If using cameras with analog or HDMI outputs for instance, you would first need a capture card to get that signal into the computer (and would need to be compatible with streaming software), and then if you wanted multiple cameras, the pro switcher would need to be in line before the capture device.
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