Create a new button (and script). Place new btn in same location of the Copy button (BT_COPY). Call that new button ""Copy"". Move / shrink the actual Copy button. Now user sees the Copy button in the same place. Place this script text in the new button.
sOrderType = """"
retVal = oBusObj.GetValue(""OrderType$"", sOrderType)
If sOrderType = ""Q"" Then
' Set the ShipExpireDate
expireDate = ""20291231"" 'whatever you want here
retVal = oBusObj.SetValue(""ShipExpireDate$"", expireDate)
retVal = oScript.SetUIControl(""BT_COPY"",""SHOW"") ' in case you hid it but resizing it to really small would work too
retVal = oScript.InvokeButton(""BT_COPY"")
retVal = oUIObj.HandleScriptUI()
End If