| Celtic Dragonlord |
I believe the critical wording is "on a successful strike". In that case, you'd need to use the weapon rules (perhaps similarly to the Flame Tongue ability?)
If it was simply as a delivery for the spell, then technically you could get away with using Wondrous Item rules. It's an object, just like a rock, a glove, or a wondrous orb. It wouldn't matter about hitting them with it like a whip (although it would be good for flavor) in that case.
And in that case, it would be a "use-activated" item, useable limitless times per day, with no body slot. Useable once per round as a standard action, as if casting the spell itself (without provoking AoO's). This would cost 4000 GP (level 1 spell x level 1 caster x 2000 GP, x2 for no space limitation), plus the cost of the masterwork whip. For more damage, she could create it at a higher caster level.
Since Shocking Grasp is instantaneous, it cannot be used (as per the basic rules) as "continuous".
So basically, there ARE ways to do it both ways, but it depends on the desired effect.