You mean... the correct way?
I got used to moto/euro style brakes a long time ago when I was motorcycling and biking at the same time - couldn't keep code switching. That is one thing I like about CRC - it is easier to get brakes with short hoses on the right lever and long hoses on the left lever.
If you do want to switch it, first check if the brake lever itself is symmetrical - the SRAM DB5s I have on my Fuse can be flipped over and installed on the opposite side. If the levers are not symmetrical, then yes, you can disconnect the hoses and connect to the opposite side. You'd follow the same procedure used for shortening the lines, except you are connecting to the opposite side.
My advice would be to make sure you have all your tools in place and ready to go so you can do the swap as quickly as possible, with as little fluid loss as possible. It is then likely you won't need to bleed.
But mentally prepare yourself for having to bleed in case more air gets into the system than intended. Don't do it right before a big ride, for instance.
EDIT: Just noticed you specified XT brakes - I don't think any shimano brakes are symmetrical, so you'll need to swap the hose connections rather than flip the levers.