Possible to use mana ability in response?
Yes, you may.
The pixie's ability is an activated ability that happens to be a mana ability as well. Unless otherwise stated, you can activate those any time you have priority, so it's possible to do so in response to Shock.

602.1. Activated abilities have a cost and an effect. They are written as “[Cost]: [Effect.] [Activation instructions (if any).]”
605.1. Some activated abilities and some triggered abilities are mana abilities, which are subject to special rules. Only abilities that meet either of the following two sets of criteria are mana abilities, regardless of what other effects they may generate or what timing restrictions (such as “Activate this ability only any time you could cast an instant”) they may have.