Soak the red onion in a bowl of ice water, 10 minutes. Drain the onion and squeeze dry.
Whisk the yogurt, dill, honey mustard, and salt and pepper to taste in a large bowl. Slowly drizzle in the olive oil and 1 tablespoon water, whisking until combined. Add the onion, ham, cheese, lettuce and apple and toss to coat. Pile the ham mixture in the middle of each wrap. Fold in the sides, then roll up the wraps. Cut in half and serve with the strawberries.