Please differentiate hands for the purposes of using equipment. Now it doesn’t matter which hand was crippled as you can still use one-handed items without a problem. Soldiers should be more proficient with one particular hand than the other, at least at the start. When you will use less trained hand accuracy penalty could be worse. It can be soldier statistic and be part of training like ‘both hands proficiency’, also artificial limbs in New Jericho could be without this penalty. And some soldiers could be ambidextrous to omit this penalty.
EDIT: Oh above relates to weapons but in case of using medkit with not proficient hand it could have some failure (no healing) value.