barring the No's, if there are any, being upside down, there's no problem with moving the shifter. You may need more cable, maybe just outer, depending on how the cable runs. If it's a standard flat bar I'd be surprised if a straight swap wasn't possible. I've done lots of messing about with bars and removing, installing, the rubber grips can be a pain. My best solution has been to use a knitting needle and some basic Weldite cyle oil.
Remove - bit of oil just short of the end of the knitting needle, let it run round needle, then insert under grip and slide round, pushing needle in further. Repeat at other end of grip then twist and it should start turning then slide off easily.
Putting on - same oil, inside grip and rotate on way on it will slide easily and allow you to position minutely on bar.
After a couple of hours it's like you've never put oil in there and the grips are set in place. This has worked with all sorts of rubber grips for me and I've never had a movement problem with them when riding.