Mister= Console Games which should be played relaxed, on a couch, over potentially several hours, with the original gamepads.
MAME = Arcade games that should be played in short bursts, standing up, with a control panel.
In general at least, this isn't a great idea you are having. I don't know why in the last month or so we've had 20 people ask this same question.
In the interest of goodwill though I'll try to assist. So I'm assuming this monitor has hdmi in for the Mister and/or the Mister supports component out? All you really need to swap out are the USB encoders then, so just do that. Plug both into a hub, put that hub, along with a usb extension cable running to each system inside the coin door or something. When you want to switch just unplug the hub and plug it into the other cable. Remember.... K.I.S.S. (keep it simple stupid). If you absolutely refuse to unplug stuff those two cables can be hacked into a switchable y-cable via a 4 pole double throw switch. Then you'd just flip a switch. Video switching should be easy so I'll leave that to you. Video switchers are a dime a dozen if you don't have enough inputs.