Very interesting contributions, thanks so much.
For the most part, we declare ourselves right or left handed depending on how we write. The only other such declarations that come to mind as being in common parlance are how we play string instruments and baseball (or, I suppose, cricket). Notably, Ringo Starr was forced to write right handed but calls himself left handed and says that it informs his playing.
I read an interesting article some years ago that refers to "mixed handedness" when folk do different tasks different ways. Besides playing right handed, I (used to) bat right handed. Another article I read on the subject reported that there's no relationship between the hand we use to write and how we hold a shovel, rake, or similar implements.
On guitar, many players who fret mostly with their left hand also fret or "tap" with the right. I occasionally do this on dulcimer 1) for certain harmonics 2) for effect, if I do it really hard, or 3) to play a pitch while I'm holding down another string with my left.
Have a great day!