No you cannot alter the currency after you have shipped. You have theoretically created an order with agreed prices, which can create an expected position in teh ledgers at shipment, so you cannot. Also if you use the confirmation, or key from an order, you have already set an agreement with the customer.
The system will not allow you to create an invoice in a different currency to the order when it has been shipped.
You need to unship it, correct it, verify the rates on each line and then ship it.
If you do not want to do this you will need to invoice them in the original currency. Failing this write a modification to allow you to do this and all of the currency revaluations and re-reading of the rates for unrealised gains and any other postings you may need to consider.