There's more to it than just which hand on the stick...
* Different sight picture, right seat vs left seat. Ask any brand new CFI
* Which hand works the avionics, part 1: Traditionally, avionics have been designed for center stack, pilot in the left seat, so that the pilot's hand doesn't obstruct the screen.
* Which hand works the avionics, part 2: on planes with glass cockpits, especially touch screens, if you're working the glass for all it's worth, switching screens, entering in waypoint names, changing frequencies a lot, would you rather be doing all that with your left hand? in turbulence?
* Some folks think "throttle should be closer" and reverse the order of the power knobs, ignoring the fact that on throttle quadrants -- choose your WWII fighter -- the throttle was always on the left, away from the pilot. And remember that even on custom motorcycles, location and function of major controls is still standardized.
* There's also the matter of possible negative transfer. Is there anything in your past that could cause problems flying right seat, or will any future flying be compromised because of all your planned right seat flying? Unlikely, but worth thinking about.
I'm now pretty much either side (CFII), either hand, wheels / sticks / side sticks, whatever. However, since almost all my time in the past five years has been left seat in the RV-9A, getting really comfortable in the right seat requires an hour of takeoffs and landings -- including looking at the flight instruments right ahead of me instead of looking across the cockpit. Then again, on this last trip, 28 RV hours, east coast to west and back, I gave dual in C172s, right seat, no problem.
The rest of the story is that transitioning to the left seat in the RV-9A took some doing, but there's more to that story. I had not flown in nine months due to highly invasive spinal surgery, had spent most of those nine months in bed recovering, and was working to get all systems going again. Plus, I had a whole bunch of distracting, new glass cockpit to learn.
As the saying goes, it's an experimental and you can do what you want. The rest of the statement is, but there may be subtle consequences that can bite you in the rear at some point.