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It might be possible to use the ShapeShifter class for this, but that will only handle the interaction with the ros::Publisher object; it won't handle the type conversion from whatever internal type you have to the correct message type.

Since you only have to handle two cases, I'd suggest making a virtual base class and a class for each type that you want to publish (obviously, types and exact code flow may differ from what you're trying to do):

class TrajectoryPublisherBase {
  public:
    virtual void advertise(ros::NodeHandle& nh) = 0;
    virtual void publish(const MyJointTrajectoryType& joint_trajectory) = 0;
};

class JointTrajectoryPublisher {
  private:
    ros::Publisher pub_;
  public:
    virtual void advertise(ros::NodeHandle& nh, std::string topic) {
       pub_ = nh.advertise<trajectory_msgs::JointTrajectory>(topic);
    }
    virtual void publish(const MyJointTrajectoryType& joint_trajectory) {
        trajectory_msgs::JointTrajectory out;
        // TODO some code to convert your joint trajectory type to a trajectory_msgs::JointTrajectory
        pub_.publish(out);
    }
};

class MultiArrayPublisher {
  private:
    ros::Publisher pub_;
  public:
    virtual void advertise(ros::NodeHandle& nh, std::string topic) {
       pub_ = nh.advertise<tstd_msgs::Float64MultiArray>(topic);
    }
    virtual void publish(const MyJointTrajectoryType& joint_trajectory) {
        std_msgs::Float64MultiArray out;
        // TODO some code to convert your joint trajectory type to a std_msgs::Float64MultiArray
        pub_.publish(out);
    }
};

main() {
  std::shared_ptr<TrajectoryPublisherBase> pub;

  if(joint_trajectory) {
    pub.reset(new JointTrajectoryPublisher());
  } else {
    pub.reset(new MultiArrayPublisher());
  }

  MyJointTrajectoryType& joint_trajectory
  pub->publish(joint_trajectory);
}