A Link cosplayer at Ratha Con was actually the inspiration for this strip. I asked if she was left-handed, as she wore the sword over her left shoulder, and she told me that she was not but wanted to keep the character accurate. I appreciated this, although when I brought it up with other cosplayers, they didn't see this decision as particularly special and expressed similar views to the above comic strip.
Personally, if I were cosplaying someone that had no access to their non-dominant left hand, I'd probably flip it. Then again, maybe not, I'm pretty good with my right hand.