Yeah, the relay used here is a very good way to go. Unless you already had a spare contact sensor, I would lower the cost further with a Xiaomi door window sensor. They're very easy to solder wires to- There it is again, MORE SOLDERING! 
The best technique for joining wires together with hand soldering or soldering to components that shouldn't get too hot, it to tin the wires with solder. That way, it's a quick 1-2 second touch of the solding iron and they're joined.
A note about this video: It's text book. In practice, I don't use a heat sink, I don't apply flux (I use rosin core solder that already includes the flux), and I move faster than what is shown in the video.
Keep your solding iron tip clean with either a damp sponge or a soft coiled tip cleaner, and use a chisle tip.
