Cthulu left right up wire fell out - help

These three wires came out and wondering if I can put them back in and make them stay some how. Will I need to sodder it back on or is there any easy way to do this?

Also, will the Hori Real Arcade Pro 3 SA take HAPP/American buttons, possibly P360 stick?

Strip the wire longer and bend it in half so its double the thickness then twist it and put it back and screw it down on the terminal strip

make sure all the screws are tight and down so the wires dont move around too. the point of it is so you dont solder, its solderless.

Does this work if the wires are already too short/barely able to get into a hole? Thanks for the fast reply. Will be trying this later with friends. anything I should look out for since I’m new to this?