As printed electronics is evolving toward applications in biosensing and wearables, the need for novel routes to fabricate flat, lightweight, stretchable conductors is increasing in importance but still represents a challenge, limiting the actual adoption of ultrathin wearable devices in real scenarios. A suitable strategy for creating soft yet robust and stretchable interconnections in the aforementioned technological applications is to use print-related techniques to pattern conductors on top of elastomer substrates. In this study, some thin elastomeric sheets—two forms of medical grade thermoplastic polyurethanes and a medical grade silicone—are considered as suitable substrates. Their mechanical, surface, and moisture barrier properties—relevant for their application in soft and wearable electronics—are first investigated. Various approaches are tested to pattern conductors, based on screen printing of 1) conducting polymer [poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS)] or 2) stretchable Ag ink and 3) laser scribing of laser-induced graphene (LIG). The electromechanical properties of these materials are investigated by means of tensile testing and concurrent electrical measurements up to a maximum strain of 100%. Performance of the different stretchable conductors is compared and rationalized, evidencing the differences in onset and propagation of failure. LIG conductors embedded into MPU have shown the best compromise in terms of electromechanical performance for the envisioned application. LIG/MPU showed full recovery of initial resistance after multiple stretching up to 30% strain and recovery of functionality even after 100% stretch. These have been then used in a proof-of-concept application as connectors for a wearable tattoo biosensor, providing a stable and lightweight connection for external wiring.