The Green Lantern oath is intrinsic to the nature of the persona. Is it necessary to utter the oath while charging one's ring on the power battery? Not at all.
However, Hal Jordan and Alan Scott each adopted their own distinctive oaths for just such occasions. Well... eventually. Initially both had the familiar "In Brightest Day... In Blackest Night" mantra, but then Alan diverged into a more succinct oath that got straight to the point.
Did this mean that his own battery charged his ring faster than had Hal's? Perhaps so since the ring and lantern were both crafted from the same meteorite. Then again, his counterpart's ring and battery were also of similar elements harnessed by the Guardians of the Universe.
Regardless, an interesting aside is that Earth-One's Tomar-Re used the exact same oath as that of Earth-Two's Green Lantern's abbreviated saying.