I don't shake bees, I trade frames. Frames of bees belong inside a hive and mixing frames from different hives will not cause fighting as long as only 1 or 2 frames of bees are moved at a time. I have moved frames of brood, pollen, and/or honey complete with bees attached from one hive to another. True the forager age bees will most probably return to the original hive if it's in close proximity but another frame of bees can be moved into the hive.
I've used this method to bolster population in a re-queened hive, add brood to a hive to stimulate an idle queen, provide empty comb to a hive that has backfilled the brood chamber so the queen could lay, feed natural foods to stimulate a weak hive, etc. I nurse 2 hives back from the brink of starvation this spring by swapping frames back and forth between the 2 hives. One was OWC, the other Russian, and they are now both 3 mediums high after dwindling down to a baseball sized mass in Mid-May.
When I do splits I usually take one frame from each of 4 hives and place in each nuc. I split that way up to 5 splits from 5 hives. The genetic diversity of such a split makes it worth while and the bees are so confused that by the time they sort things out....they're all one hive.