-Can you please dispatch the remainder of our order?
'can' if you are, say, uncertain whether the supplier is in a position to meet your request e.g. if is waiting on supplies himself from overseas, in order to fulfill your order.
Would** you please dispatch the remainder of our order (at your earliest convenience?
Making a request of the person (to accommodate your wishes)
'balance' would used if referring to money. Hence, a deposit might have been received, and you write, requesting payment of the balance of the account.
** 'could' is also a possibility. It is also used to make a polite request.
Student or Learner