IMHO, healthy people don't get diabetes because they consumed x grams of sugar in their ketchup on occasion. If you're eating an otherwise healthy diet, I don't think a small amount of sugar in a condiment will do you in. Unless you're that metabolically deranged, then by all means do what you need to do. Otherwise, gluten-free, real-food does just fine.
Heinz organic ketchup (organic tomato concentrate, organic distilled vinegar, organic sugar, salt, organic onion poder, organic spice, natural flavoring) Got it at Walmart.
Grey Poupon Dijon Mustard (water, vinegar, mustard seed, salt, white wine, fruit pectin, citric acid, tartaric acid, sugar, spice) Also from Walmart. I don't care for mustard, so I only use it in small amounts in homemade dressing.
Lea & Perrins Worcestershire Sauce (Distilled white vinegar, molasses, water, sugar, onions, anchovies, salt, garlic, cloves, tamarind extract, natural flavoring, chili pepper extract) Walmart
San-J Gluten-Free Tamari (water, soybeans, salt, alcohol) Sprouts/Whole Foods/Central Market/Market Street
Can't help you on mayo, as the hubs and I both find the stuff disgusting. Also can't help on barbecue sauce--I'm from Texas.