I used to believe that braided was better than solid because of the surface area. A well-seasoned and well-educated fellow ham in my area told me that a plain old copper wire, the larger the better, works just as well if not better for RF.
Cutting the coax can and usually will affect what the SWR meter shows, but it does NOT affect the actual antenna SWR. The only thing that can change the SWR at the antenna is something that directly affects the antenna itself (or the grounding), IE relocation of the antenna, trimming or adjusting the antenna, damaged antenna, mounting stud issues, etc.
One other note, using coax with poor shielding will give a lower-than-actual SWR reading, as the RF leakage/loss occurs both going and and coming back in. This makes the reflected power lower at the meter than at the antenna. This will be more of an issue with longer runs of cable such as on a base station, but not as much of an issue with the short lengths used on a mobile.