After washing down the chain with WD40, I happened to spot the little bottle of Hoppe's #9. Before I knew, I was applying the lube on the o-rings, counting each link to 114. The amount of oil that went on the chain was, I think, only a few drops in total. So, I bet there is not much oil to fling off. The bottle looks like the white bottle in the picture.
Hoppe's 9 - Lubricating Oil
The thin rod made it possible to dispense very little to each link. Well, I am not sure if the oil itself will ruin the o-ring or not. Once the bottle is empty, I am going to refill it with some gear oil.