Doing the IR before the CPL is very common, I can't remember the exact figures but you only need something like 70 hours PIC to do the IR, so people often do it first then sort out the CPL after.
You are quite right in that once you complete your CPL, if you don't have 200 hours total time, you would need to build some to get the CPL issued. However, if you're doing the whole thing in one go, you can do the CPL, then immediately start the IR without getting the CPL issued. Then, when you finish the IR you have your 200 hours total time, and get the whole thing issued in one go, again a very common way of getting this done.
The main thing I would worry about is which theory package to do. The CPL+IR exams are quite tough as two packages, and a lot of schools don't offer a very good package to take them. This is because the vast majority of people go straight for ATPL exams. If you have any intention at all of looking for a multi crew or airline job in the future, the ATPL exams make a lot more sense, as it will save you having to redo a load of exams in the future. Once you have the ATPL exams you have 3 years to get both CPL+IR, so it's up to you as to whether this time scale works for you.