I'm a bit paranoid at the moment, and I don't like doing anything that might screw up my save games. I saved after using Kyne's Peace, but before the shout cooldown completed (a few seconds remained). When I reload it cools down just fine...but was it safe to save at that point, with just a few seconds left? Could it potentially muck up my save and future gameplay in some manner?

Doubtful

What will screw up your saves is overwriting a slot over and over.

About 10 is as far as I go, then I make a new slot, I also never use Autosaves, any of the features.

What it should do is load up with the remaining time on your cool down meter, as all other timed scripted events act the same way if I save during them.

I don't overwrite slots, I just make lots and lots of saves. I even have them all moved out and backed-up elsewhere.