"送牛奶用的手推车" can be translated into English as "milk delivery cart" or "milk cart (for delivery)".
"Milk delivery cart" directly conveys the purpose of the cart (for milk delivery).
"Milk cart (for delivery)" is a more concise version, with "for delivery" in parentheses to clarify its use if needed, though often the context makes it clear.
Both expressions are commonly used and understood in English-speaking contexts.