I'm going to buy Yongnuo RF-603 II, but I'm confused. Will it work with my flash, a Shanny SN600N (specs here) or not?
Yongnuo's RF603II triggers are manual-only, so they will work to fire any flash that has an ISO-compliant foot, with the firing pin in the center of the foot's "square". You probably can't tell this from the specs, but you will be able to tell by pictures of the flash's foot.
The Shanny SN600N has that, so it will fire in sync remote if you have one RF-603II as a transmitter on your camera, and another one on the flash's foot to act as a receiver. It has no built-in radio receiver.
But. With these triggers, it will only fire in sync. You will not have TTL, FP/HSS, or remote power/zoom/groups/settings control over the flash. All you can do is fire the flash remotely and wake it up remotely if it goes to sleep.