My Chevy came with a reducer and I've been using the standard shaft for my Equal-i-zer WD hitch with no problems at all for over 3 years now. (and I've towed that trailer a LOT!)
The only problem I encountered was finding a locking pin long enough to go through the entire receiver. But I finally found one. (I keep a lock pin and the reducer in the receiver shaft all the time).
You may notice a bit of "bumping" after a while. I found the holes in my original receiver hitch on the truck are slightly bigger than the holes in the actual hitch shaft OR the reducer. I think they made bigger holes for a bigger (circumference) pin. Using the standard pin that fits the holes in the hitch shaft and the reducer now has movement (slightly) in outside hole of the truck receiver. When pulling forward, or stopping quick, the hitch actually moves slightly, causing a slight, "bump" sound. Nothing to worry about, just takes a little time to get use to it.
Of course, if you can get a hitch shaft the same size, that would really be best. But the reduce will work fine.