Add the mayo, vinegar, sugar and grillin' shake to a bowl and whisk. Taste, and adjust ingredients to your liking. One note, it will get a little sweeter as the sugar disssolves in the mix, so don't go overboard.
Add slaw mix to bowl and pour in dressing, a bit at a time. Using tongs, mix the slaw with the dressing until the cabbage is lightly coated with dressing.
Refrigerate for 30 minutes. Lightly stir before serving.