You don't need to replace your cart buttons; the only settings that would affect a product's Add to Cart button code would be Item Number, Variants/Variations, or Suggested Price (if you're using "Let buyers edit price").
The discount would be applied in the cart. If you configured your discount with a Discount Code, then the buyer would need to enter that code in their cart to claim the discount. If you left the Discount Code blank in the discount's settings, then the discount should be applied automatically once a buyer's order meets the Min. Item Total and/or Min. Items in Cart thresholds you defined for that discount.