A popular tactic in my home games is to channel Shocking grasp through a metal weapon. The obvious benefit is to add the spell damage to the weapon damage. And if the weapon has reach even better. Put a copper wire in a whip ....
So the question is: Would this be League Legal?
Sounds like that would be a DM call so I wouldn't count on it. Since the spell says it comes from your finger (and some archtypes/builds are designed specifically around delivering touch spells through a weapon), I know I wouldn't allow it at my table unless you had a class ability that let you do it.
It clearly goes against the intent of the spell so I would rule against it. Twisting RAW to gain a clear benefit above and beyond the rules intent is simply bad form.
It cannot be performed RAW because;
1) Casting Shocking Grasp require you to take the Cast A Spell action
2) Attacking with a weapon requires you to take the Attack action.
Which means its two seperate action and even if you could take more than one action in a turn say with Action Surge, it still wouldn't be possible because Shocking Grap's duration is instantaneous. It's cool if your DM let's it fly at his table, but i don't see it as easily done in Organized Play.