We report the study of novel biodegradable electrospun scaffolds from poly(butylene 1,4-cyclohexandicarboxylate-co-triethylene cyclohexanedicarboxylate) (P(BCE-co-TECE)) as support for in vitro and in vivo muscle tissue regeneration. We demonstrate that chemical composition, i.e., the amount of TECE co-units (constituted of polyethylene glycol-like moieties), and fibre morphology, i.e., aligned microfibrous or sub-microfibrous scaffolds, are crucial in determining the material biocompatibility. Indeed, the presence of ether linkages influences surface wettability, mechanical properties, hydrolytic degradation rate, and density of cell anchoring points of the studied materials. On the other hand, electrospun scaffolds improve cell adhesion, proliferation, and differentiation by favouring cell alignment along fibre direction (fibre morphology), also allowing for better cell infiltration and oxygen and nutrient diffusion (fibre size). Overall, C2C12 myogenic cells highly differentiated into mature myotubes when cultured on microfibres realised with the copolymer richest in TECE co-units (micro-P73 mat). Lastly, when transplanted in the tibialis anterior muscles of healthy, injured, or dystrophic mice, micro-P73 mat appeared highly vascularised, colonised by murine cells and perfectly integrated with host muscles, thus confirming the suitability of P(BCE-co-TECE) scaffolds as substrates for skeletal muscle tissue engineering.