When a creature regenerates all damage is removed from it, and if it is attacking or blocking it's removed from combat.
Assuming I shock him during my declare blockers step it would be removed from combat before it got a chance to deal its damage.
Regeneration removes from combat, so no, the damage from Horned Troll will not go through.
Rule 614.8: Regeneration is a destruction-replacement effect. The word instead doesnt appear on the card but is implicit in the definition of regeneration. Regenerate [permanent] means The next time [permanent] would be destroyed this turn, instead remove all damage marked on it and tap it. If its an attacking or blocking creature, remove it from combat. Abilities that trigger from damage being dealt still trigger even if the permanent regenerates. See rule 701.11.
It's also tapped when it regenerates incidentally, so I could shock it before it attacked.