The LED is the current throw king:
It puts out small but useful enough 450 lm (peak, probably not possible with 10180).
The optic is a very throwy one and has the right size. A reflector should work well too, but I found precisely 0 intensity measurements coming from manufacturers, so I use TIRs in my drawings. I may use Endermann’s calculator though…
Frankly, I don’t know whether driverless is a good idea.
This LED had a very low Vf. It’s totally unsuitable for direct drive with moderately sized batteries, but 10180 may not blow it. It will be hard on battery and hard thermally. A regulated driver might be a good option, but it will take a lot of space, 2-sided for sure. A FET driver will be smaller, but when doing FET why don’t go all the way and make it driverless?
EDIT: I see very roughly 40 kcd with the calculator, again at peak intensity.