OK, being in the US myself, I didn't know if there were other issues in other countries, so I didn't want to offer advice that might get someone electrocuted.
I've built a few of these, but I don't recall off the top of my head exactly where I put the ground wire from the line cord, but as I said, it should be obvious where the main ground is once you get in there.
I think it also wouldn't be a problem to replace it with another two wire cord. Good grounding is obviously better, but you should be fine either way.
Edwin