With a 12 V power supply, 12 V may even have a hard time conducting the currents.
What I think is missing is a LED that indicates that the correct amount or some current is flowing . e.g. that there is a significant drop across the regulator. It's too easy for nothing to happen without that. The currents may be hard to achieve.
This part:
https://www.electro-tech-online.com/custompdfs/2012/06/3092fb.pdf might be a better part to use, but the resistors may have to be recalculated. Another suggestion is a DC-DC converter which would give you better battery life and a higher consistant voltage. The important issue is that it be battery powered.
if you go to
www.digikey.com, you can look select an appropriate fuse and look at the data. When a fuse pops is dependent on many factors.
7 to 10 mA is considered a lethal current when it's applied across the heart muscle so damage to the skin could occur (burning) if the current was exceeded by lots. Adding a small flame proof resistor such as 100 ohms would offer more protection, but make sure the fuse will blow.