Suppose a shrimp has been put on the ground that has just been taken out of water. Now touch the shrimp from a distance by a stick. The shrimp will jump straight upward. Will the shrimp do any work in this case?

Yes, the shrimp does do some type of work because according to Newton's third law, every action has an equal yet opposite reaction force.
In this case, the stick is the action force and nudges/pokes the shrimp. The shrimp then reacts and exerts an opposite yet equal force by jumping in a straight, upwardly manner. So, yes the shrimp does do work in this case.