This Dayton Audio DC28F-8 1-1/8" Silk Dome Tweeter is an amazing tweeter. I have used it several times in various installations. I have removed various amounts of it's flange to accomodate existing hole needs without changing the sound. I have also cut a slit an a length of automotive heater hose and slid the hose around the flange to provide a gasketed shock mount.
I have also used it in new installs where I routed the opening and recessed into the baffle board. My point is that it has always been versitale and quality. So long as you do not modify into the working portion of the speaker and only trim the flange you will be fine.
I think that there perhaps may be some minor change in the sound if material is removed, but I have never noticed a difference in a system. I would suspect that in order to actually hear a difference the entire system would need to be under good testing conditions and pro audio analysis equipment.