You cannot take either the CPL or IR skills test without having passed the relevent theory first. The hours refer to the amount of study needed for the relevent theory for each part. Most people who are aiming for ATPL status do all the theory exams together before starting the CPL course as they are not much more than the CPL exams and cover the theory for the IR as well.
I think you may have Integrated and Modular mixed up! It is possible to start a modular course with a PPL complete but some integrated providers may make you start from scratch. My advice to you would be to begin the ATPL studies on a part time basis, while continuing to save via your work.
Best of luck