The constant and vigorous flow from the pumped wort greatly expedites the chill. A spoon creating a whirlpool is better than nothing, but the pump forced whirlpool is much more effective. I don't believe there is any type of less expensive submersible pump that would perform the whirlpool. A $99 Chugger pump is the way to go for this operation.
It is easier to do things right the 1st time rather than to explain why it wasn't when you have to do it the 2nd time.