There's only 5 volts Direct Current running through a keyboard controller. You'd feel more touching a phone wire (24 volts idle, 50+ volts ringing) or a 9 volt battery.
Unless you touch the wires to your tongue, you likely won't feel anything.
Be careful about "picking a random ground" however. Depending on the quality of your home wiring (e.g did the previous owners do it themselves or was it contracted/inspected), they may have goofed up neutral and hot or neutral and ground, therefore if you connect the ground to a ground on the frame that also attaches to the AC side of wiring, you may have whats called a "ground differential" that may cause a rather significant ~60 to 120 volt AC shock, and/or fry stuff.
Granted, sounds like you're working on a PC emulator and not a real arcade machine, so you're already totally protected by the sealed PC "switching" power supply.
However, if talking real games, I know this from experience... One of my bedrooms downstairs was WIRED BACKWARDS. Neutral was hot and hot was neutral. Plugged in my machine, powered up... Nothing. Touched the coin door to check the service switch inside... OUCH!!!!!!! 120 volt shock! (tested to ground with a tester). Thank goodness it didn't fry the PacMan machine I plugged in, or I would have filed suit against the previous owners (seriously!) since they clearly never had it properly inspected.
After a strong amount of cussing, I powered down and rewired all the outlets in the room correctly. And then took the neon tester to every other outlet in the house and found that only that room (that the previous owners "finished" themselves) was wired backwards.
GRRRRR....