So, here we are. The IKEA OMLOPP-lighting system looks great and is tailored to IKEA's kitchen system. It's also quite expensive, with €25~€35 for each drawer, so I was set on making something myself.
I already gathered I would use a microswitch to detect an open drawer: those things are cheap, quite reliable and tiny. I also considered using reed switches, but those are quite hard to come by in a NC-configuration at a decent price level. Spending the same amount of money on one switch as the cost of one LEDBERG strip kit is kind of defeating the purpose of doing it on the cheap, so that was right out.
Getting rid of the wiring is a simple case of routing a small slot on the outside of the cabinet: those slots won't be visible once the kitchen is assembled, which makes for an aestehic finish.
Now to figure out how to mount the strips and the switches.