You can create a table that has only one field which is not named the same as any other field in your application - let's say selectedDim. This field should have the values: Country, Gender and Agegroup.
Then you can use $-sign expansion to put any of these selected and non-assosicated values in as the name of a dimension.
For the dimension the expression could be: =$(=MinString(selectedDim))
You can create a filter pane that you make rather small - then you get a drop-down. The user might multi-select so you will have to use MinString. If the users hold the CTRL key while selecting they will always do a single-select.