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, Honey Mango Blonde, Belgian Wit with orange peel and heather tips, New England Style IPA
Primary 1: Empty
Primary 2: Empty
Primary 3: Barrel Aged Old Shredsputin
Primary 4: Bourbon Barrel Conceited Dick
Secondary 1: Nirvana on Cedar (a Utopias inspired brew)
Secondary 2: Nirvana on Oak (a Utopias inspired brew)
Secondary 3: Ginger-Peach Melomel