You can also do this on the Mixup Cube; it's a bit harder to fix there.
I have a pretty cool sequence to fix this on the Mixup cube. First I used setup moves to put all edges in the right orientation into the 4 center spots so that a single slice is an 8-cycle of edges which fixes the parity. Then I undo the prepatory setup moves which leaves the puzzle in the cube shape and then I undo the resulting cycle in the edges which is a nice symmetrical sequence.
I could dig up my Mixup Cube and demo this if anyone is interested.