Yes, this can be done using Cognos Report Studio.
First, build a report in Cognos Report Studio that accepts user inputs as parameters. You would have to use Parameters as objects in your query while creating the report. When you run this report, it should prompt the user to supply the inputs to these parameters. Make these parameters mandatory.
After testing this report, go to the main report and set up drill through options. Select the previous report you created as the child report. It should prompt you to map the parameters to the variables in the parent report. If the mapping is done correctly, it should give you your desired functionality i.e. when you click on a % cell, it should pass appropriate values to the child report and display the child report.