If you have the same model as shown in your ebay link, i'm pretty sure that you have to remove these four screws only to remove the metallic cover of the fan case and nothing else. These screws do not connect the fan with the cooler. The screws just connect the metallic cover of the fan to the case of the fan.
If you are able to remove this metallic cover, you should get to the inside of the cooler fins easily. If you remove this metallic cover of the fan, both, the cooler and the fan can still be mounted inside the notebook, but you get access to the inside of the cooler fins to clean them.
The metallic cover, which i mean, covers the outer parts of the fan blades and the inner side of the cooler fins. It is the part where the bar code label (300-0001-1276-...) is sticked on. You should not have to disassemble the whole cooler to clean it as far as i can see at the ebay picture.