How does cloud drake's buff function for champions without an ultimate ability?

The cloud drake buff (Cloudbringer's Grace) reduces the cooldown on the transformation spells champions like Jayce, Elise, and Nidalee use, so it essentially functions as normal. It just feels a bit different because these champions naturally have low "ultimate" cooldowns.

As a special case, Udyr instead gains global cooldown reduction based on the number of stacks of this buff he has, equal to the amount he would normally get if he had an ultimate. Shyvana, whose ultimate is only accessible once she gains 100 Fury, gains additional percentage Fury generation from all sources based on the number of stacks of this buff she has.

Cloud Dragon Soul, which increases a champion's movement speed once they use their ultimate, operates normally on all champions except Udyr. As Reddit user phroxz0n, a Riot employee at the time, explains on this post, Udyr gains the additional movement speed from this buff on all of his spells, and is the only champion who currently does so.