Toss shredded cabbage and 1 teaspoon salt in a colander or large mesh strainer set over a medium bowl. Let stand until the cabbage wilts, at least 1 hour or up to 4 hours. Rinse cabbage under cold running water (or in large bowl of ice water if serving immediately). Press, but do not squeeze, to drain; pat dry with paper towels. (Can be stored in zipper-lock bag and refrigerated overnight.).
Stir together lime juice, zest, oil, vinegar, honey, cumin, and cayenne in medium bowl. Toss cabbage and red pepper in dressing. Season to taste with salt; cover and refrigerate until ready to serve.