As a lefty I use my mouse in my left hand and remap the keys to the right side of the keyboard. I use IJKL for movement and usually mirror the mapping of most of the standard keys -- U in place of E, O in place of Q, Y in place of R, comma in place of Z, etc.
This left handed setup actually has an advantage in that there are more keys available at the right side within reach of your starting position, such as the brackets, backslash, forward slash, backspace, hyphen, and equals keys.
Even the Ins, Home, and other keys over to the right are good for certain special actions if I run out of keys near my starting position. I like this better than feeling my way across the character keys since, with the exception of the raised tab on the F key, it's hard to feel your way over there without looking away from the screen. So I can map actions to the Home or Delete key, the arrows or the numpad, and immediately feel where those keys are without looking away. But even this isn't usually necessary because of all the surrounding keys already available.
And of course as with a right hander I can still map to the left side of the keyboard, too, if I need to. I can usually reach my index finger to the T, G and B keys no problem.
The only pain comes in when certain games don't let you remap at all, or are selective about what you can remap, but most developers worth their salt will include full remapping. I've had to use AutoHotKey to set up keyboard macros but it hardly ever goes that far -- the only cases so far were Stick of Truth which is otherwise an awesome game so it was forgivable (I hope The Fractured But Whole is better in that regard), and No Man's Sky but I gave up on that for other reasons. Macros are always an option in any case. There is a community of helpful people and sample scripts (some even ready-made for your game) if you want to go that route.
Anyway, I hope this helps someone or inspires another lefty to return to his or her roots and stay true to the cause. Heh...
P.S. Even right handers could have more keys available to them by using ESDF instead of WASD. I'm not sure why that ever became the standard; it's not even where you rest your left hand naturally on the keyboard. There are groups out there encouraging ESDF, like use-esdf.org.
