You can get creative with the form factor of your touch control. Any non-conductive material will work as a base -- here I chose a wooden disc that I had from a craft store -- just make sure it's something to which the copper tape will stick well.
With the alligator clips and copper tape you can form the capacitive touch pads in any layout or pattern you like. Plus, since you don't need direct finger-to-copper contact for the touch to register, you can cover the copper pads with something more attractive, such as fabric, paper with a printed UI design, even a canvas with painted artwork.
QT Py Mount
To begin, mount the QT Py near an edge of the board so that you'll be able to plug in a USB cable for power and HID data.
I used a Glu Dot to affix it.
Plug in the STEMMA QT wire to the QT Py and the MPR121 breakout.
Clip the alligator wires to the breakout board's twelve connectors.
Cut a 2" segment of copper tape and remove the protective paper.
Fold over one end a small amount to give the clip something to bite into a little, then stick the strip to the base, folding a bit of excess around to the other side.
Continue doing this for each connector. Then, you can add some additional tape to help things stay put.
The larger surface area of each pad will give you a larger target for your touch interactions as well.
You can use the controller as is, or add a graphic overlay on top of the copper touch pads. You don't need to touch them directly for them to work!
Here's a sample graphic I made if you'd like to use it as a launching off point.
Print your graphic and cut it out.
Use spray mount adhesive, or a glue stick, to affix the overlay to the board.