9 V battery = bad choice, low power.
Another choice, 12 white SM LED's in series, one 300 ohm R, 3 AA or 3 AAA alk. batteries, & boost converter.
3 AA's & boost need 7 X 5 X 1.5 cm. Adjust V output to desired brightness, about 5 mA?
I used this with a " holiday " hat, but only 4 LED's in series & 3 AAA's. Boost is size of 2 AA batteries side by side; might find smaller one to go with AAA's.
Another choice, 12 white SM LED's in series, one 300 ohm R, 3 AA or 3 AAA alk. batteries, & boost converter.
3 AA's & boost need 7 X 5 X 1.5 cm. Adjust V output to desired brightness, about 5 mA?
I used this with a " holiday " hat, but only 4 LED's in series & 3 AAA's. Boost is size of 2 AA batteries side by side; might find smaller one to go with AAA's.