I believe the LED on board is a bright white LED, with a forward drop of around 3-3.5 V and they seem to run it at 1A (no additional resistance, it is powered by the switching IC driving constant current through the LED).
I wanted to provide roughly the same behavior - rectification properties and voltage drop, so I used a standard diode and series resistance. The diode to rectify and resistance to bring voltage roughly within assumed range (knowing it was a 1A supply). I presume merely using a 3.5 ohm resistor by itself would also work, likely needing at least 1W, better at 3W or more (knowing that fully on it would be burning 3.5W, but assumed blinking and rare usage may allow less power capability)
I soldered mine back up and put it back together. I will report again if anything doesn’t work (yesterday it was a bit of an alligator clip experiment).
I am considering buying some Cree parts from digikey, I suspect they would work ok - XPEBTT-01-0000-00T80