Hitching a charged, albeit worn, NP-BX1 lithium battery to the astable multivibrator produces a blinding flash:
The current pulse shows the wearable LED really takes a beating:
The current trace is at 100 mA/div: the pulse starts at 400 mA, which seems excessive even to me, and tapers down to 200 mA. It’s still an order of magnitude too high at the end of the pulse.
On the other paw, maybe a 14% duty cycle helps:
The top trace shows the base drive voltage dropping slightly, although I suspect the poor little transistor can’t take the strain.
The LED really does need a ballast resistor …