First I opened up the box of the electronics that came with the LED stripe. I saw that there is a lot of unused space and I just had the idea "this could be enough for a nano". In fact it seems like the box is designed exactly for this. ;)

On the back side of the PCB I soldered some wires on it: Ground was easily detectable (big copper area, two pins of the 12 V adapter) and the third pin on the connector for the power supply had to be  12 V. Measuring the switched on device with a multimeter confirmed this assumption. Arduino nano can just handle 12 V,  and will generate 5 V anyway - I'm lucky! So I don' t need to use an extra 12 to 5 V converter.

The three drivers/transistors for the R, G, B LEDs are on the left side and cables have already been connected to their collector pins to sink the current through it. Instead of adding my own transistors I wanted to use these existing ones. I just had to cut the lines from theis bases to the IC that controlled them. After cutting one copper line I had the idea to just remove the pins on the controlling IC and use the pins pad to solder on my cables to let arduino control the LEDs.

I tried out some resistor values for my Darlington touch sensor schematic on the breadbord and soldered it onto a small piece of board that was lying around. The piece was exactly big enough to place all parts but small enough to fit into the box - in addition to the arduino! I'm so lucky!