I take my chains off my wick and run some hot water with mild, all natural dish detergent (Seventh Generation is what it's called) in the sink and soak it for about 5 minutes. Then I scrub/swish it around shortly and rinse. This is what I do regularly after burns, but it has worked when I've gotten K-1 on my handles before.
Even though it's a gentle solution, it's effective plus hasn't harmed anything. If handles are leather, I'd recommend following it with some saddle soap to put the moisture back into it and let it dry. Mine aren't leather, but I've cleaned many a saddle and it's not a bad idea.
Edit: I have the pro-series chains too and my first paragraph works great on those handles especially, just make sure to rinse them well out of the handles and wrap/squeeze with a clean towel then let air dry. You should be good to go!
