I think it depends whereabouts you're going within those countries, Dontcallmelove. We went 12 years ago and our stay apart from around the Iguazu Falls was pretty urban, Buenos Aires, a bit of Uruguay and Rio which aren't risky places for Yellow Fever. I covered myself in Deet insect repellent because I'm prone to insect bites, I've had worse at home than there. I'm glad at the time we couldn't get hold of the Yellow Fever vaccine due to their being bought up wholesale by various corporations, or that's what we were told and yes I've heard the side effects can be quite nasty. It didn't present a problem us not having had the vaccine, in fact we weren't ever asked if we had when we were there.
I hope you enjoy your stay there as much as we did. It still remains one of my best holidays ever.