I'm not sure if there is a way to do this in the original connection pane until you've hidden the fields you don't want to use in the worksheet. What I would do is navigate to the worksheet, hide the columns you don't want, and then extract the data then.
I think hiding fileds is a good solution actually.
Tableau states that hiding a set of fields before extracting the data is one of the way to reduce the size of the extract.
Please follow the link for detail: http://kb.tableau.com/articles/howto/reduce-extract-size