Spell-Storing weapon + Magus’ Spellstrike

Okay, I’ve seen a few questions about this but not the exact question I have so I figure it’s reasonable to ask.

Let’s assume the following situation, I have a magus with a spell-storing weapon with, let’s say, Frigid Touch stored in it. I enter combat and cast Shocking grasp using my standard action, move to my target and use Spellstrike to take the free touch attack I get with Shocking grasp to deliver the spell through my weapon.

Assuming I hit, I deal weapon damage + the damage of Shocking Grasp, let’s assume a 5th level magus wielding a rapier and say this is 1d6 piercing + 5d6 electricity.

As I have hit my target with my weapon and dealt weapon damage, can I now use a follow-up free action to discharge the stored Frigid Touch using the Spell-Storing element of the weapon for an additional 4d6 cold damage and a chance to stagger the enemy?

Or do I have to choose to discharge the stored spell OR use Spellstrike?