smelly catalytic converter?

My 90 RAM just started to stink which I assume is the cat gone bad, rotten egg smell. The truck runs fine and we don't have smog tests here so I have no intention on shelling out money to replace it. I was just going to weld in a straight pipe where it was but my lazy side started thinking. Does anybody know how long that stink will last before it burns out? Needless to say it would be easier to just leave it there but I can only live with the smell so long and I'm sure it can't be great for you inhaling it