I think that handedness can be regarded as a scale - some people are very one-handed and others closer to ambidextrous. I am strongly left-handed. I made the decision early on in my musical career to accept the limitations of that. I play guitar left handed, piano accordion upside-down, even reverse the hands on a whistle.

Having learned a mandolin (strung in fifths like a fiddle) upside-down, taking advantage of the GDAE becoming EADG and using all my guitar chords straight away, I have tried a righty fiddle inverted.

Most of the dexterity required is definitely in the bowing hand. I can play with the instrument nearly vertical in the crook of my arm, which enables reasonable fingering, but vibrato is more challenging. I have, however, found that playing it upright on the knee (like a small cello) works well and puts the higher strings on the bowing-hand side.