Hello,
As Harvey wrote, use a transistor as a switch, but add a zener diode as well, which can limit the voltage to the LED (It will burn up fast if you send too much power to it) The Zener diode will allso make sure that you don't send power the wrong way and fry your detector)
The circuit for driving the LED is build into all cheap flashlights - maybe you can use one, and then replace the switch on the flashligt with the diode and the transistor?
Measure the output from the detector, to make sure that you are not sending so much power that you destroy everything. A diode will lower the voltage with about 1.5 volt. - read the schematics for every component to get it right.
You really need an osciliscope to measure what you get from the detector, a capacitor might be needed to smoothen out the signal before you send it to the LED.
Don't blow up your detector, dump your schematics and calculations on a electronics forum, before you let the blue smoke, out of your detector.
GL - it sure looks like a fun project.
/Steffen