Yes, but if it was the water pressure regulator popping open and shaking the pipes when the water pressure in the house dropped, wouldn't that happen when drawing both hot and cold water, and with every other faucet in the house as well; including the toilet ballcock opening to flow when you flushed the toilet?

Why would it only happen when opening the kitchen sink faucet to draw cold water?

If it were me, I would buy a "mechanic's stethoscope" for about $15 at any place that sells mechanic's tools.

http://www.americantechnology.co.uk/...4006-120-p.jpg

Touch the steel probe of the stethoscope to the cold supply line while a helper opens the faucet and confirm that the noise is coming from the cold water pipes, and not actually from the hot water supply piping.

I'm wondering if you have crossflow through that faucet, and by opening the faucet to draw cold water, you're shutting off the flow of hot water through the faucet body, and THAT's what's causing the water hammer in the hot water supply piping?

With the mechanic's stethoscope, you can move upstream of the faucet to hopefully find the section of pipe that's moving and bouncing off the nearby studs or drywall, and secure it better. For $15, it's a very handy tool to have.