I don't like saying go low tech, but I'd have to agree with Ryan.
I have so many battery devices, and just today one had semi-died. It wasn't reporting door open, but was still reporting temp/etc. Had no clue, and took a while to figure out what was wrong as it was showing recent activity. Then I looked again, and it said battery "30%", which often means "battery 0%". Got a drawer full of batteries now, semi-expensive and all difference sizes. You'd likely have 2 batteries... the contact sensor and the light. So, I'd have to agree to avoid that.
Some device that uses standard batteries, and only turns on when the contact is open (cupboard door), via old fashioned wire is probably best