You're right that irregular bleeding is typical during perimenopause and that it's a common warning sign of gynecological cancer. The fact that you're in perimenopause does not mean you can't also have cervical, ovarian, vaginal, endometrial, or uterine cancer too. In fact, many of these cancers become most prevalent between ages 45 and 65. But it's also true that most irregular bleeding is not a sign of cancer. Only your doctor can assure you that your current bleeding pattern is no big deal. Depending on your particular situation, your doctor will likely do a pelvic exam and run some blood tests, and maybe request a biopsy or an ultrasound. You may also be asked to wait a few weeks or months to see if the abnormal pattern continues before you have more tests.
If a biopsy or ultrasound indicates that you're unlikely to have cancer, take that as reassuring news; however if the abnormal pattern continues it's your job to keep bringing it up to your doctor. Some cancers take years to develop to the point where they can be detected. If abnormal bleeding continues, you may need to be repeatedly retested. About a third of premature malignant growths are discovered on the second, third or fourth round of testing. The trick here is to be vigilant without assuming the worst. Chances are, this is nothing to worry about—but you want to keep this issue on your doctor's radar screen.
Finally, you should be able to bring up any concern with your doctor without fearing ridicule. If you don't feel comfortable doing that, it's time to think about finding a new doctor.