The book I'm reading, "The Complete Joy of Home Brewing" says just to add the priming sugar/syrup to the bottom of the bottling bucket and siphon the beer right in. That being said, anything more than that (i.e. whirlpool idea) should be more than adequate to mix. If I'm not mistaken, the reason you don't want to stir too much is because it will add oxygen.
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On Tap: Raspberry Saison, Belgstralian White IPA, Bourbon Barrel Conceited Dick
Primary 1: Kohatu IIPA
Primary 2: HBC 438 SMaSH
Primary 3: Barrel Aged Old Shredsputin
Primary 4: Geest Belgian Golden Strong
Secondary 1: Nirvana on Cedar (a Utopias inspired brew)
Secondary 2: Nirvana on Oak (a Utopias inspired brew)
Secondary 3: Ginger-Peach Melomel