You are correct, this can be done with a parameter. Just add a calculated field and you're set.
The parameter will have the list of dimensions from which to choose, and then use the calculated field to display what is chosen.
Please see the attached Superstore workbook where I've mocked this up.
If you wanted multiple dimensions you could just have multiple parameters and add to the rows shelf.
Hope this helps!
Book1.twbx 1,020.6 KB