Polyhydroxyalkanoates (PHAs) are biodegradable polymers synthesized by certain bacteria and archaea with functions comparable to conventional plastics. Previously, our research group reported a newly PHA-producing bacterial strain, Rhodococcus pyridinivorans BSRT1-1, from the soil in Thailand. However, this strain’s PHA synthase (phaC_Rp) gene has not yet been characterized. Thus, this study aims to synthesize PHA using a newly engineered bacterial strain, Cupriavidus necator PHB⁻4/pBBR_CnPro-phaC_Rp, which harbors the phaC_Rp from strain BSRT1-1, and characterize the properties of PHA for skin tissue engineering application. To the best of our knowledge, this is the first study on the characterization of the PhaC from R. pyridinivorans species. The results demonstrated that the expression of the phaC_Rp in C. necator PHB⁻4 had developed in PHA production up to 3.1 ± 0.3 g/L when using 10 g/L of crude palm kernel oil (CPKO) as a sole carbon source. Interestingly, the engineered strain produced a 3-hydroxybutyrate (3HB) with 2 mol% of 3-hydroxyhexanoate (3HHx) monomer without adding precursor substrates. In addition, the 70 L stirrer bioreactor improved P(3HB-co-2 mol% 3HHx) yield 1.4-fold over the flask scale without altering monomer composition. Furthermore, the characterization of copolymer properties showed that this copolymer is promising for skin tissue engineering applications.