Place cream cheese and cold pack Cheddar cheese in a microwave-safe bowl; slice cheese into chunks with a knife. Microwave cheese in 30-second intervals on high just until softened, stirring between intervals.
Stir red onion, Worcestershire sauce, black pepper, paprika, and hot sauce into cheese mixture with a fork until evenly combined; spoon into an airtight container and refrigerate, 8 hours to overnight.
Remove cheese spread from refrigerator about 30 minutes before serving.