I am with
@berndo here.
Cordless lights are enough at C1 level; I think if you want to do the course with a cordless light, it's gonna be okay, although at least one day, the instructor will probably ask you to dive with a canister light to show you can manage the hoses during the S-drill. However, because managing hoses and wires is still a crucial skill - speak with the instructor first
I am sure some cordless lights are good enough even for "easy" C2 dives (2h, maybe even 3h dives - depending on the burnout time of the light), and switching battery between dives is an option.
As usual, speak with the instructor before the class.
I actually PREFER cordless lights in caves - since the risk of losing it is remote compared with OW, and there is less complication due to the lack of wires. Technically speaking, they are ok also for deco OW dives, but I do not like the idea - if by accident I lose it during the deco stop, it's over, no way I will go back to retrieve it. It is an extremely rare circumstance actually, but not unheard of. Anyway, it's a personal preference, not a necessity.
Power in caves is usually not the biggest factor -I often run in low power. The shape and focus of the light beam (or whatever you call it) are more crucial factors.