SimGuruGrant confirmed that you can’t choose whether your Sim is left or right handed, but that such preferences happen randomly.
Wanted to clarify left versus right handed Sims. It’s not something you can choose, but there’s a chance your Sims will be left handed. This basically just means Sims will prefer to use their left hand to say, pick up a beverage. They might also be right handed. Hope that’s all clear!