Left-handed people (of Western upbringing) who were adults the 1960s were all forcefully re-trained as children to only use their right hand for writing, as prejudice considered using the left hand "bad", resulting in adults who were quasi-ambidextrous. So this might be a handy fan-canon explanation why, while the in-game models all hold their weapons with the right hand in first person view, you occasionally get scenes in the Meet the Team videos or things like Medic's playing-bonesaw-like-a-violin taunt where they hold items in the way a left-handed person would.
Admittedly, when Medic holds the bonesaw in his right hand and then places the tip to his neck like a violin, of course he would use his left hand to mimic the motions of a violin bow, as the model animation does not switch the weapon to a different hand first. And some scenes in the MtT videos might be explained by rules of scene composition in a Western left-to-right format, forcing the animators to put the weapon into a left hand, i.e. BLU Medic defending himself against the RED Spy in Meet the Spy, with his back to the audience so that the audience can then see the RED Spy's transformation. (On the other hand, I'm sure the animators could have composed the scene while putting the weapon into the Medic's right hand. So why did they do it this way?)
Other scenes are quite interesting, too, for example when BLU Engineer clearly reaches over with his left hand to pull his pistol from its holster on his right hip! You can't tell me that's not deliberate.
BLU Sniper in Meet the Spy uses his kukri with his right hand to defend himself, however. But maybe only because he grabbed it with his right hand after he had turned around. It was lying on the crate on which would have been his left side before. And he holds his Sniper rifle like a left-handed person, with his left hand on the stock and the butt against his left shoulder. I never noticed that before. But again that might be caused by scene composition, because the animators wanted to show the Sniper in the lower left part of the picture and the Spy appearing behind his shoulder, on the upper right side of the picture.
I would have suspected the animator may have been left-handed themselves and subconsciously put the weapons there, if the RED Spy had not been so clearly right-handed. Except of course for catching and putting on BLU Medic's falling glasses with his left hand. Darn it. Well, Spy is a method actor; if the BLU Medic is secretly left-handed, the Spy would imitate that.