Powering the light with a 3S LiPo battery (11.1 V, or 12.6 V fully charged) should probably work, given that the LED driver circuit is in the light and not in the wall wart (unusual, but happens).
That voltage regulator might not work though, as these modules typically need an input voltage several volts higher than the output voltage. You could use it to step the voltage down from a 4S or higher LiPo battery (up to 40 V, which means up to 9S).
Using a 3S-pack, you may even get away without using a voltage regulator at all, since 12.6 V from a fully charged pack is very close to the 12 V of the wall wart.
You will need some kind of low voltage detection for your battery pack though, otherwise you will damage it when completely discharging it. Accoustic warners or miniature voltage meters are fairly cheap though.
Do you have access to a regulated power supply? You could test how low the voltage can be to still power the light. If it still runs below 11.1 V you definitely need a low voltage warner.
I’m no expert on this topic btw, so please join in everybody if I talked nonsense.
Good luck with your build, maybe show us a picture when you’re done.
CircaM, that buck board is a decent one, i have a few knocking about which get used on various things and what you’ve chosen to use won’t be fine for that, one of these step up down dc-dc converter (there are cheaper one on their)
is what you want to keep a 12v supply from one of those lipo packs, quick video showing what a Step up or down dc-dc converter does
but you will not get massive amounts of runtime from one battery. You can buy 2 packs and use a parallel lead to make one big 12.6v pack with double the amps though e.g. Parallel lead
i have used rc lipos for what your planning to do on bike lights and it’ll be fine, you will however need one or two of these Lipo BatteryLEDLow Voltage Buzzer Alarm
Or you run the risk of destroying one of the cells before you even know about it, they can take a beating but only so much before one of the 3 internal cells starts to not take a proper ampage charge even when balanced.
Just don’t parallel two different voltage batteries EVER!, different amped batts are fine though.
Ooops, I nearly forgot, if you want it to be all plug and play and very easy to use, you’ll need two of these, one on the out side of the board to go to the light, and one on the end of the batt parallel lead to the board male connector
And one of these to go onto the input side of the buck board female connector
Edit 3:32pm, Fixing links as requested.