There are many euphemisms in this list, few of which I've heard. I'd probably get the drift if someone used any of them.
I don't see the reason for the specificity. If I am going to excuse myself for such purposes, I might say I'm going to visit the washroom (or little boy's room), and if there was any reason to say so, I might indicate I could be a few minutes-- just so others are not putting their jackets on and lacing up their boots in the expectation of my return within less than sixty seconds. Or perhaps I'd let the Sunday New York Times (City Edition) under my arm say it for me.
If you're going to tell them the nature of the elimination, perhaps you should also include the information that you intend to thoroughly wash your hands in case some fecal matter should contaminate them. Perhaps share information on the consistency and regularity of your bowel movements? I just don't see the need for it.
If you're going for the comedic effect, on the other hand, try using "massive dump".