The side you play isn't going to protect you from cheap shots.
It can certainly hurt you. D-men playing their off-side are quite often blind to the play around them and reliant on their partner. If you're not comfortable at the NHL speed or fully aware, you can get hurt easily on your off-side.
I know you know this, but if you're a lefty playing right-side D, and the puck gets pushed into your corner, not only is your back turned, but if you want to push the play up the ice (rather than wheel around your net), you need to go backhand to forehand, pivot to face the play, look up, make a decision, and play the puck.
That extra step, backhand to forehand, could be half a second, which is the difference between being hit, and not being hit. And, if you're hit while you've got your back turned to the play, you're not braced for it, because you never saw it coming. And this isn't just specific to a guy boarding someone else with a cheap shot, it can be a guy coming down your boards that hits you shoulder to shoulder and puts you in a bad way because you had to take that extra moment to put the puck on your forehand.
Why rush Skjei to play right-side in the top4, and bring down his partners (L-L [and R-R] pairs do not perform as well as L-R), instead of just letting him ease into the game on the third-pairing? Can give him heavy o-zone starts against weaker competition with good teammates.
O-zone faceoff? Zuccarello line with Skjei pairing.