Yeah, that works too. Very old joke and I've told it a few different ways in the past.
The funniest time was when I told some Frenchmen I was dating. He understood it and loved it. Later on, he told some American friends of his and...well....a lot got lost in translation. He ended up making me retell it to these people who said what he told them was something completely different and made no sense whatsoever. Okay, guess you had to be there.