Time-Resolved Emission (TRE) is a truly non-invasive technique based on the detection of intrinsic light emitted by integrated circuits that is used for the detection of timing related faults from the backside of flip-chip VLSI circuits. Single-photon detectors with extended sensitivity in the Near Infrared (NIR) are used to perform time-correlated single-photon counting measurements and retrieve the temporal distribution of the emitted photons, thus identifying gates switching events. The noise, efficiency and jitter performance of the detector are crucial to enable ultra-low voltage waveform sensitivity. For this reason, cryogenically cooled Superconducting Nanowire Single-Photon Detectors (SNSPDs) offer superior performance compared to state-of-the-art Single-Photon Avalanche Diodes (SPADs). In this paper we will discuss how detector front-end electronics parameters, such as bias current, RF attenuation and comparator threshold, can be tailored to optimize the measurement Signal-to-Noise Ratio (SNR), defined as the ratio between the switching emission peak amplitude and the standard deviation of the noise in the time interval in which there are no photons emitted from the circuit. For example, reducing the attenuation and the threshold of the comparator used to detect switching events may lead to an improvement of the jitter, due to the better discrimination of the detector firing, but also a higher sensitivity to external electric noise disturbances. Similarly, by increasing the bias current, both the detection efficiency and the jitter improve, but the noise increases as well. For these reasons an optimization of the SNR is necessary. For this work, TRE waveforms were acquired from a 32 nm Silicon On Insulator (SOI) chip operating down to 0.4 V using different generations of SNSPD systems.