i voted for ambidexterous, since that fits the best, but isn't the exact case.
i would call myself "cross-dominant", which means that, depending on the situation, i am considered either left-handed, right-handed or ambi.
for example, i write and use computer mice right-handed, but i use my phone left-handed, eating with utensils is ambi, though i prefer the knife in my left hand, since i'm better in controlling my right (by training).
i throw with left, but catch with right, and deflect with either.
when greeting someone with a handshake, i will extend whichever hand is more practical in that situation, if i happen to have my right hand occupied (with a drink, for example), i will extend my left hand for the shake without thinking about it, but when holding a snack (which i hold left), i will extend right.
if both hands are free, i will extend the hand that is not facing the person (if he stands slightly to my right, i will extend the left hand, slightly left, i extend right).
i have had comments on that, but that's just me, i dont care mostly, but some tasks are trained into prefering a certain hand, like, my preferred drinking hand is left, since right usually has either the PC mouse, a pen/pencil or a fork in it.
also, my finger-preference is a bit jumbled up, i use my middle finger for a lot of index-finger work, and often need to actively remember to point with the index (pointing with the middle finger is deemed inappropriate)