The tech appears to run off Critical Charge, which doesn't trigger at all for weapons in the left hand, so sadly this is a no-go.
As to spellcasting with the right hand, there's a secondary element, which is player input. You click and hold to charge the spell, but it doesn't release automatically - you release the mouse button (or whatever console players use, probably R2) and the spell fires. Even if spellcasting is faster in the right hand, I don't think it makes a big difference because the spell only fires as fast as you charge and release it, and that extra release is essential.
The tech appears to run off Critical Charge, which doesn't trigger at all for weapons in the left hand, so sadly this is a no-go.
As to spellcasting with the right hand, there's a secondary element, which is player input. You click and hold to charge the spell, but it doesn't release automatically - you release the mouse button (or whatever console players use, probably R2) and the spell fires. Even if spellcasting is faster in the right hand, I don't think it makes a big difference because the spell only fires as fast as you charge and release it, and that extra release is essential.