Barrie has proven it as much, if not more than Bigras has... so it isn't all lefties. Tyutin looked bad on the right of JMFJ, but has looked decent with others throughout the years on the right side.
I fully understand the difference and risks. It just isn't all that uncommon for lefties to have to play the right side, it is a lot more uncommon for righties to play left. You can go through the NHL and see a number of lefties that play the right frequently or prefer it... Hammer, Coburn, Beauch, Phanuef, Goligoski, Depres, among many other lefties have played a significant chunk of their time on the right and done really well. The advantage for the Avs, is the player that likely has to play their off side (I don't see EJ and Barrie on the same pairing), it likely on the bottom pairing. The minutes will be limited.
I disagree on Barrie. I don't think he's proven himself as much as Bigras has, because Barrie didn't have the same defensive responsibilities in junior as Bigras, so he didn't face the same challenges. The challenges that face defenseman in the NHL having to make such quick decisions, isn't the same in junior, especially for an offensive rover like Barrie who had much more room and time to do his thing against weaker defensive players, and systems.
I think it's possible he can pull it off, and I'd like to see it given a shot now because of the way the D is structured, as opposed to the past where they didn't have many good second pairing guys outside of Barrie. If it works, it would allow Beauch to play with Z on the second pairing, giving them two solid pairings for the first time in forever. It would also lead way to what I think could be a good second pairing in the future with Zadorov-Bigras, after Beauch moves on.
As for the the D in the league that can play their off side, it's still a small percentage. The guys that can do it well have a spotlight put on them in these discussions, and it's forgotten how many guys can't do it well. They can do it in a pinch, but there's enough discrepancy between their natural and off sides, to make teams put them back where they play their best. Just off hand, I would guess it's around 15% (give or take) of D in the league can play their offside well enough to do it full time.
With all the D men that have come through the Avs in the last ten years or so, there's really only been about six D men that have played their off side well enough to do it full time, and some of those are debatable as to how well they did. Clark, Leopold, Hannan (briefly), Stuart, Beauch, and now possibly Bigras.