Overall, and as a left-handler myself, I think Mikhail may well have been left-handed, but Nicholas right-handed.
Are there any pictures of Mikhail playing tennis? I think that would be the clincher as George VI was forced to write right-handed, but still played tennis left-handed.
Ann
There are significantly more ambidextrous lefties than their naturally right-handed counterparts as well. Some of this probably evolved out of necessity. Lefties have - at times - carried with them a societal stigma as has been pointed out on here. With the overwhelming majority of people being naturally right-handed it also makes sense that left-handers would need to prove more adaptable. Those left-handed desks from back in my school days come to mind. Few and far between. Buildings, tools and devices through history have largely been design to accommodate a right-handed world.
I remember reading some about the evolution of the sprial-staricase and how in Medieval times nearly all were constructed clockwise for the inhabitants of the castle better guard against intruders. If you're carrying a sword in your right-hand (being right-handed) it makes it more difficult to attack if the right side of your body is bumping up against a curved wall. Those defending against you by contrast can wave the weapon in their right-hand free.
But my favorite example of this is much closer to home for me. Growing up my next door neighbors, Kevin & Matt, were naturally lefties but learn to throw a ball and eventually bat right-handed largely because of the influence of their older right-handed siblings. At a young age they borrowed their old siblings baseball gloves instead of getting their own, which of course fit onto their left hands, forcing them to learn to throw with their right. Imitating those siblings, and other kids in the neighbor like me, they also learn to become more proficient swinging a bat from the right side than left. However when it was time to sit down at dinner or do school work the fork or pencil was in their left-hands, not their right.
Baseball in particular really puts on display the prevalence of natural lefties who have had to adapt in some form or another. Whereas you often see people who hit from the left side and throw with their right hand it is far less common for the opposite to be true (of course there are a number of "switch-hitters" as well). There is a slight advantage to being a left-handed hitter in baseball being as how more pitchers throw right (easier to see the ball if you're batting from the left side and adapt to breaking pitches such as sliders and curveballs), and also because you are a full step closer to first base and therefore have a slightly better chance of beating out an infield hit. Conversely the only position in the field where it is beneficial to being left-handed is first base...indeed there hasn't been a left hand throwing catcher, second-baseman, shortstop or third baseman in decades in the Majors, and the outfield positions have no significant advantage or bias towards righty or lefty fielders.