I installed my rim tape then noticed was too wide so I trimmed it with a razor knife. Would this have caused any damage to the rim bead?
You can though I can say that in 40+ years or riding and many years of working in shops I've never once had to do this. Rim tapes come in various widths from various makers so you should be able to find one that will fit. Also a little too wide is far preferable to a tape that is a little too narrow.