Polyurethane is mechanically very strong, but has the chemical weakness you expect from it being an ester: it hydrolyses in hot water, has limited resistance to heat, strong bases, strong acids. Not my spontaneous choice for electrochemistry.
PVC resists acids, hot water, and is less bad at heat. With plasticizers it gets soft, though not exactly a rubber. It's the usual insulator for common electric cables.
Some electric cables use PVDF or ETFE as an insulator. Usually at coaxial cables for high frequencies, but they would resist heat and chemicals, nice for electrochemistry.
Industrially used polymers are extremely numerous, so recognizing them needs experience. The most common ones can be recognized by their aspect, contact, smell. When possible, a precise density measurement tells a lot. Burning a sample is very informative, especially to someone trained to recognize the odour.