If you're just wanting a special button that lights up that LED and that's it, then yeah it's cake. The only tricky thing about wiring the LED to the 9-volt battery is that the 9-volt battery has an internal resistance that is difficult to figure out... you would need to know that info to figure out the best resistor to use on the LED. That is, you would if it's the usual kind of LED...
One thing about the LED... you said it's a "5 volt LED". LEDs are confusing things... usually you don't have a "5 volt LED", you have a "20 mA LED" or a "30 mA LED" - they specify the current needed, not the voltage. But, if you bought the LED in a little package by itself and it said "5 volt LED" on it, that usually means that the LED has an internal resistor that lets you hook it directly to 5 volts without needing any other components. If that's the case, you're good to go - I just had to make sure there wasn't any confusion about it.
If you have the internal-resistor-5-volt-LED thing, all you need to do is put a 4v Zener diode next to the LED and you can hook it up to 9 volts. That, or you can put five or six normal diodes in series, and put that between the battery and the LED. Same thing. (try six, if too dim, cut one out and use 5.) Normal diodes are easier to get, but putting five or six in is extra work - if you can get a 4 volt Zener diode it saves you a little bit of soldering.
In terms of shocking people, you just can't do that with only 9 volts. You can't even do it with 12 volts. 110 volts gives you a strong but not very damaging buzz in your arm, and leaves the muscles kind of twitchy for five minutes or so, so I guess somewhere in the 35 to 60 volt range is where you start feeling that there's electricity present. However, there's several inches of plastic between the surface of the button and the microswitch, and even more plastic between the surface of the microswitch and anything connected to electricity, so even if you had the button connected to 200 volts nothing would happen to people pushing the button.
Finally, you can put the components in any order you want. You can do (battery+) --> (diodes) --> (LED) --> (switch) --> (battery-), or you can switch those around in any order. The only important thing is the diodes and LED - the sides of the diodes that have the little stripe on them have to point towards the negative lead on the battery. (That is for normal diodes. If you found a 4v Zener diode, it is very important that its little stripe point in the other direction - towards the positive side of the battery.) Also look at the LED, and you will notice a flat side - the LED wire that is close to the flat side must go towards the negative lead on the battery.
If you are using normal diodes, then nothing happens if you wire it wrong. If anything is in backwards, the LED just won't light, and you just flip a component around and try again, see if it lights, repeat until it works. If you have a zener diode and you wire it in backwards, the LED might burn out when you push the switch.
And, that will get your LED to light using a 9 volt battery. However, I don't think that a single LED will be enough to light up your picture. You can put several LEDs in parallel if they are the 5v-internal-resistor kind, and they will all light up at once. Just use larger diodes if you do. (like 1/2 watt diodes, 1-watt diodes, 2-watt diodes... you need 1 watt for every 9 LEDs.)
You can also use the 5v connector in your computer, and not need to use diodes at all. You would connect between the red and black wires.