Rob,
While I don't have much experience with non-vinegar based slaws, I do think you could modify the recipe below to get what you're looking for. I think replacing the cider vinegar with a blend of champagne or rice vinegar would bring the acidity down to a manageable level.
From
www.smittenkitchen.com , via Gourmet Magazine
Dead Simple Slaw
Gourmet, June 2008
This slaw is both sweet and tart, surprisingly bold for the small number of ingredients. While it goes perfectly on top of pulled pork barbecue, I like it on the side as well.
2 1/2 lb green cabbage, cored and cut into 3-inch chunks, then finely chopped or shredded
1 medium onion, finely chopped
1 large green bell pepper, finely chopped
1 large carrot, coarsely grated
1 1/4 cups mayonnaise
1/3 cup cider vinegar
2 teaspoons sugar
Toss all vegetables in a large bowl with 1 tsp each of salt and pepper. Whisk together mayonnaise, vinegar, and sugar, then toss with slaw. Chill, covered, stirring occasionally, at least 1 hour (for vegetables to wilt and flavors to blend).
Slaw can be chilled up to 1 day.