Recently, CsPbX₃ (X = I, Br, Cl) perovskite nanocrystals (NCs) have drawn wide attention owing to their outstanding photophysical and optoelectronic properties. However, the toxicity of such NCs remained a big challenge for further commercialization. Herein, we adopt facile methods for synthesizing green-emissive Cs₃Cu₂Cl₅ and blue-emissive Cs₃Cu₂Br_2.5I_2.5 perovskite NCs that exhibit broad emission spectra with large Stokes shifts. These NCs showed photoluminescence quantum yields (PLQY) up to 65% (Cs₃Cu₂Cl₅ NCs) and 32% (Cs₃Cu₂Br_2.5I_2.5 NCs) with limited stabilities. To further improve the stability, the NCs were blended with a hydrophobic polymer poly-methylmethacrylate (PMMA) and embedded inside the polymer fiber by an electrospinning process to form composite fibers. The as-prepared Cs₃Cu₂Cl₅@PMMA and Cs₃Cu₂Br_2.5I_2.5@PMMA fiber films demonstrated good surface coverage and better thermal stability, and even retained their emission properties when dispersed in water. The emissive fibers were also deposited on flexible polyethylene terephthalate (PET) substrates that displayed high resistance towards bending and twisting with no signs of breakage, damage, or loss of optical properties. Finally, UV-pumped phosphor-converted WLEDs fabricated by using these blue and green-emitting fibers revealed CIE chromaticity coordinates at (0.27, 0.33) with a maximum luminous efficiency of 69 Lm W⁻¹ and correlated color temperature (CCT) value of 8703 K. These outcomes can be beneficial for the development of futuristic flexible display technologies.