We report on the structure and optical manipulation of the director configurations in emulsions of liquid-crystalline droplets of a compound exhibiting the nematic (N) and the twist-bend nematic (N-TB) phases. We demonstrate a decrease in the ratio of the bent elastic constant K-33 to the splay constant K-11 by nearly 2 orders of magnitude with decreasing temperature in the N phase. The director structures in liquid-crystal droplets doped with a photo-switchable surfactant without and under ultraviolet (UV) light are discussed in light of the strong elastic anisotropy of the investigated compound. We also compare our findings with the results obtained in doped nematic droplets of a conventional 4-cyano-4'-pentylbiphenyl (5CB) liquid crystal. The dynamics of droplets in the N-TB phase by UV light irradiation are also studied using polarizing and confocal microscopies.