Sorry, there is no way to do that at this time. I agree that would be nice to have and will add it to my list. I actually just ran across that limitation myself recently.
As a workaround, you could create the missing columns in the target table, perform the data copy, then drop them afterwards.
Or, if the number of rows to copy is on the small side, you could go to the editor, write a query to select only the columns of interest, export that to insert statements, then run those in the target database.
If you want the 2 tables to have the same data, another option (probably the easiest one) is you could use Database -> Compare -> Data. You can select which columns to include there.