I understand your feelings and I would be nervous too but this was done in my home, in front of me by someone who's doing this every single day as that's his job. I also trust him, he would never do any harm. Now I know changing the battery is not complicated but you need the right tools, which I don't have.
I had my keyboard repainted last year and waited till the warranty expires to be able to give it to my tech guy. I did not trust the service provider. Better safe than sorry.
You are absolutely right. Being safe is more important than anything else. That's why I always try to go to the same place and try to make them trust me and make them be trustworthy.