From what I have read before bottling, the preferred method of priming the beer for carbonation is to add sugar or malt to the fermented beer and then bottle. I take it however that you are not supposed to stir it. In my mind that is not going to give good distribution of the sugar. How is this step to be done??
Or, another alternative would be to boil the appropriate amount of priming sugar/malt (dme) in water, transfer that to your bottling bucket, then start siphoning the fermented beer on top of that. The action of siphoning will stir it all up for you.
I snake my tubing around the bottom edge of the bottling bucket and after I have a couple of inches of beer flowing from the auto siphon from my fermenter I slowly pour the priming sugar mixture into it. Having the tubing around the edge causes a slow swirling of the beer and sugar which helps to mix it. I then take my (sanitized) stirring paddle and use the handle end to stir it slowly after the beer has been transferred. Using the paddle end mixes too quick for my liking.