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: Belgstralian White IPA, Bourbon Barrel Conceited Dick, HBC438 SMaSH, Barrel Aged Old Shredsputin, Geest Belgian Golden Strong
Primary 1: Grapefruit IIPA
Primary 2: Shred's Brown Eye Ale
Primary 3: Chocolate Orange Port
Primary 4: California Pinot Noir
Secondary: Ginger-Peach Melomel