I had a rear tire replaced but it was installed reverse of the rotation arrow. It was installed using a "newer" technology machine but that didn't go very well. During the frustrating process of removal & reinstallation, the tire got flipped & installed the wrong way. Anyway, the place where I had it installed was an hour and one half from home & it was Saturday. By the time I returned home & noticed the rotation issue, it was too late to return to the shop by closing time (although the guy said he would wait for me to return). So. I contacted the local shop (really, I wish I would have trusted this "local" guy in the "first place") and he said to bring 'er on down. He removed the tire, flipped it over and installed it back on the rim in about 3 minutes with only "old school" leverage tools with plastic guards (no pnuematics or hydraulics involved), and no further damage to the wheel. The wheel flaws grab my attention from time to time but I guess I can live with it.
It can be done, but I also have heard that cutting the tire of is the safest way. Installation with a tire machine is a snap, it's the removal that is the real pain and potential damaging part of the process.
Choose wisely, you might not be pleased when the job is complete.
Good luck!