I think using player handicaps was a good idea, assuming simplicity and consistency are high priorities.
However, this will stack with everything: Claws +10 will now give +13, so if you wanted it to only give a bonus to the base damage, an ability might work better - you could use an ability with a percentage attack bonus, maybe a 100% chance critical strike that does 130% damage, and disable it for the player at dawn/start and then enable it at dusk.
Another thing (depending on the game) you might want to add is a buff, even if it's just a dummy icon, so that opponents (or even the player) can be reminded when they select a unit that has the active bonus.
EDIT: I think Critical Strike would actually cause the same problem of it increasing other bonuses as well, and the only other ability I can think of is Command Aura, and no one likes to sacrifice an aura.
I might look around later for an ability solution, but I'm a little busy..