That won't matter at all. They will figure it out and your case can be rejected for misrepresentation. So do not have this impression that your travel history is solely based on the information presented in your current passport. They can easily see that you were in Pakistan by say your work experience. Also information on electronic passports are well stored on databases, it is easily retrievable.
My suggestion, make your full effort to get police certificate, if they are denying to issue it, try getting their response on email. Document it.
Rest, seniors shall be more helpful.
Thank you..