Not sure what the automod did with my message there, but I'm not re-typing it now. If you can bring it back and delete this one, that would be appreciated.
Summary:
Each rank of cooldown reduction (from a shrine or shop) appears to add roughly 0.5 seconds of cooldown time to items and dash/jump.
With six ranks, I had a ~13 second grenade, and ~10 second dash. I then tested a bunch more with 2x and they appeared to add ~1 second.
I've tested it with the default/first loadout (111), on both maps, and it appears to do it every time, with no other than the initial skills chosen.
V0.2.5.50