We report the room-temperature growth of vertically aligned ternary BiSbTe$3$ nanowires of diameter ~200 nm and length ~12 μm, within flexible track-etched nanoporous polycarbonate (PC) templates via a one-step electrodeposition process. BiSbTe$3$ nanowires with compositions spanning the entire range from pure Bi$2$Te$3$ ($x$ = 0) to pure Sb$2$Te$3$ ($x$ = 2) were systematically grown within the nanoporous channels of PC templates from a tartaric-nitric acid based electrolyte, at the end of which highly crystalline nanowires of uniform composition were obtained. Compositional analysis showed that the Sb concentration could be tuned by simply varying the electrolyte composition without any need for further annealing of the samples. Thermoelectric properties of the BiSbTe$3$ nanowires were measured using a standardized bespoke setup while they were still embedded within the flexible PC templates.