The same but I add dissolved sugar to the secondary fermenter. Stirring doesn't seem to disturb the sediment too much. The good thing for me is that the bottling wand fits onto the tap of the fermenter which lets me fill bottles with no foaming.I boil the prescribed amount of sugar (I use table sugar) with water or beer (about 500ml). This is so the sugar mixture will be easy to distribute into the beer. So when carbonation occurs, you get no flat and no over-carbed beer.
I put that mixture in the bottom of the bottling bucket and then siphon onto that. I place my siphon tubing along the curved edge of the bottling bucket at the bottom to promote a whirlpool. I have no objection to gently stirring the beer to ensure the sugar/water or beer mixture is evenly distributed.