You can "cheat" by copying the Slicer to the drill through page and then sync'ing them when prompted. If you don't want to see the slicer on the second page make sure the detail table is on top (bring to front) and make the background 0% transparent
Rather than modifying the background of the slicer, I think the surest thing to do, is to make the slicer invisible. you can do this by sélecting the "Sync. slicer" option in the View menu, then clic to the slicer you want to hide and deactivate the view option in front of the slicer on the diffents pages (the option is the one with the eye, the other is the sychronization option).
But, don't forget to leave at least the slicer visible on the main page, othewise you won't be able to select any value.