Context. Metal-poor massive stars are assumed to be progenitors of certain supernovae, gamma-ray bursts, and compact object mergers that might contribute to the early epochs of the Universe with their strong ionizing radiation. However, this assumption remains mainly theoretical because individual spectroscopic observations of such objects have rarely been carried out below the metallicity of the Small Magellanic Cloud. Aims. Here we explore the predictions of the state-of-the-art theories of stellar evolution combined with those of stellar atmospheres about a certain type of metal-poor (0.02 Z_⊙) hot massive stars, the chemically homogeneously evolving stars that we call Transparent Wind Ultraviolet INtense (TWUIN) stars. Methods. We computed synthetic spectra corresponding to a broad range in masses (20−130 M_⊙) and covering several evolutionary phases from the zero-age main-sequence up to the core helium-burning stage. We investigated the influence of mass loss and wind clumping on spectral appearance and classified the spectra according to the Morgan-Keenan (MK) system. Results. We find that TWUIN stars show almost no emission lines during most of their core hydrogen-burning lifetimes. Most metal lines are completely absent, including nitrogen. During their core helium-burning stage, lines switch to emission, and even some metal lines (oxygen and carbon, but still almost no nitrogen) are detected. Mass loss and clumping play a significant role in line formation in later evolutionary phases, particularly during core helium-burning. Most of our spectra are classified as an early-O type giant or supergiant, and we find Wolf–Rayet stars of type WO in the core helium-burning phase. Conclusions. An extremely hot, early-O type star observed in a low-metallicity galaxy could be the result of chemically homogeneous evolution and might therefore be the progenitor of a long-duration gamma-ray burst or a type Ic supernova. TWUIN stars may play an important role in reionizing the Universe because they are hot without showing prominent emission lines during most of their lifetime.