No, in Pickware Admin you can't change or reassign the shipping method of an order after the fact. Instead, you switch the shipping method when you create the shipping label in the WMS App. So that the warehouse knows which shipping method to use, you first add a note to the order.
How to let the warehouse know
You enter the note for the warehouse as a pick instruction on the order before it is picked:
Open the order in Pickware Admin and switch to the Detail tab.
Under Custom fields → Instructions, enter a pick instruction, for example "Please ship with express", and save the order.
The WMS App displays the note during picking. When creating the shipping label, the warehouse switches the shipping method.
You can find out how pick instructions work in How do I add pick and pack instructions to orders?
What else you should know
If an order was captured completely wrong, you can cancel it in Shopify, refund it, and recreate it with the correct shipping method. It receives a new order number in the process.
Pickware takes over the shipping method during the first import of the order. Later changes in Shopify do not arrive in Pickware. If an order shows "No shipping added", no shipping method was taken over during the import. You can find the reason in How are shipping methods from Shopify taken over into Pickware?