I also am a ripper. I even rip my printed borders to make sure the print comes out right and even around the fussy cut border. I never cut afterwards. If I need a 2 1/2 strip that is what I tear. Been doing it for over 25 years, never with a problem. No wavy borders, the threads aren't a problem. In fact I cut 4 1/2 borders yesterday. I had more little treads than when I tear. Once you tear you can pull one sring the length and that is is. I have a bunch on long eyelashes on my border from the ones I cut, after you have worked with them a while. I always shake my quilts after finishing to shake off loose threads. Boy that is when I saw all the loose little threads on my rotary cut border, not so on the ones I have torn.
Ripping borders does not do anymore damage than the threads that are broken when you sew a seam. Where do most garments and quits wear? Around the seam. Sewing does a lot more damage than tearing. Don't be afraid. LOL My grandmother tore all her strips. She has been dead 40 years and died at 80. I still have her quilts no more wear than any quilts I have made in the last 20+ years.