The power button of my Lumia 930 is broken. For now, this is not a problem as it will automatically reboot if the battery is empty and I start to charge it again. But now I want to change the battery and fear that this completely bricks my phone. Does the behavior explained above also apply to a battery exchange? Is there any other mean for powering on my Lumia 930?
There's basically 5 ways to reboot a phone of which I'm aware of. Two of these 5 ways requires the power button and the third one is simply removing the battery which I believe isn't possible with the Lumia 930. So you have three solutions left which I can think of:
Replace and fix your power button on your phone.
Use an app to reboot/restart your phone. Maybe this will help: http://www.wpxbox.com/app-to-restart-windows-phone/
Let your battery drain to absolute zero percent and then charge it again, but then you might need the power button to turn the phone on again. So I don't recommend this option.
Your easiest option is to get the power button repaired and fixed. The second easiest option would be to use an app and then restart your phone via software.