Note: This thread is meant to be beginner friendly. If you are an advanced learner, please be kind by using easy bunpo and putting furigana on the LV6+ kanji by using the following html! ありがとう
左手: Left hand
つかう: to use
つかえる: can use
両きき: both-handed
Note
I used 左手もまあまあつかえます instead of 左ききでもまあまあです because 左きき means left handed. If you are right handed, but you can still use left hand pretty well, then it should be 右ききですが、左手もまあまあつかえます, or something like that. If your both hands are really well, then you can say you are 両きき (both-handed).
It’s grammatically correct, but 大多数と同様に sounds a bit too formal to fit in this sentence. I’d rewrite it to something like:
ほとんどの人と同じで、わたしは右利きです!
わたしは、多数派の右利きです!