Photonic integrated circuits (PICs) have enabled novel functionality in quantum optics, quantum information processing and quantum communication. PICs based on Silicon Nitride (Si3N4) provide low-loss passive components and are compatible with efficient superconducting nanowire single-photon detectors (SNSPDs). For realizing functional quantum photonic systems, the integration with active phase-shifters is needed which is challenging at the cryogenic temperatures needed for operating SNSPDs. Here we demonstrate a cryo-compatible phase shifter using a low-voltage opto-mechanical modulator and show joint operation with SNSPDs at 1.3 K. We achieve a half-wave voltage of 4.6 V, single-photon detection with 88% on-chip detection efficiency (OCDE) and a low timing jitter of 12.2 ps. Our approach allows for operating reconfigurable quantum photonic circuits with low dissipation in a cryogenic setting.