The size of the jacks you referenced was somewhere in the 6mm range which I think is probably the metric equivalent of 1/4" so the size may be correct, only trying them will tell for sure. Yes the software needs to change because the pedal you are going to use is the opposite (normally closed when your pushbuttons are likely normally open) of your current push buttons. Again as with the switches 2 pins or 4 pins doesn't matter you only have to get the connections correct. Again as with the push buttons there will be a connection between two of the pins, from the picture of the jack you showed I think it likely that the two pins to the rear of the jack connect together (and thus one wire wants to go there) and the two front pins connect together and the other wire goes there. From the picture again it looked like the metal contact runs across the body of the connector to the other pin, if so one wire wants to connect to either of those pins and the second wire wants to connect to either of the other pins. What you don't want is to connect both wires to pins that connect to each other. That won't break anything, but it also won't work (as the connection will always be made even if the switch is pressed). I don't think the tutorial you referenced is a good bet. Having looked at it it appears to me to be shorting the pins in the manner I just described and if it is confusing me, I don't think its a good plan for you 
. Come to think of it an easy test for this is to use one of your leds. Replace the ground wire on one of the leds (where the other lead of the led goes through the resistor to 5V) with the two wires from the socket. With nothing plugged in to the socket the led shouldn't light (because the circuit is open) plugging in the pedal should cause the led to light. With the pedal plugged in, operating the pedal should make the light go out.
Peter