Since the proper solution (T4225) may take some time, a workaround would be to deploy this from the binary assets published on gh (https://github.com/prometheus/statsd_exporter/releases/tag/v0.22.5 currently).
This means replace the deb package deployment (in puppet) by the deployment of needed files (/usr/bin/prometheus-statsd-exporter, /lib/systemd/system/prometheus-statsd-exporter.service and /etc/default/prometheus-statsd-exporter).