/diy/ - Do It Yourself

So I have a small arduino nano project. It's supposed to be a wearable around the wrist and therefore I need to power the arduino.
There's two problems:
First: I never powered any arduino project externally before, so pic related is the basic idea. I'd need a chip and a battery to power it and be able to charge that battery. Any recommendations for that? What do I need to look out for? I thought about a small Li-ion cell, but that's where problem 2 comes into play:
I'd wear this while sleeping. Li-ion cells start burning when punctured and I'd rather not have a mine strapped to my arm and wake up to burns. Should I still go with Li-ion? Should I use another battery type? Should I stick with it? any otther security measures I should take?
Thanks for any help.

So I have a small arduino nano project. It's supposed to be a wearable around the wrist and therefore I need to power the arduino.
There's two problems:
First: I never powered any arduino project externally before, so pic related is the basic idea. I'd need a chip and a battery to power it and be able to charge that battery. Any recommendations for that? What do I need to look out for? I thought about a small Li-ion cell, but that's where problem 2 comes into play:
I'd wear this while sleeping. Li-ion cells start burning when punctured and I'd rather not have a mine strapped to my arm and wake up to burns. Should I still go with Li-ion? Should I use another battery type? Should I stick with it? any otther security measures I should take?