The route through Cockermouth differs from the C2C only in that you are heading from north to south, instead of vice versa (the detail map, right, has north at the bottom and south at the top).
You arrive near Jennings Brewery and head up Main Street, passing the Tourist Information and Toy Museum before taking a sharp right and heading towards Popcastle. There are plenty of things to do and lots of excellent places to eat and drink, which are covered in detail in the C2C section of this guide.