You'd just send a UDP packet with a spoofed source address and forget about it. There's no need to open any sort of 2-way connection for data that's only being transmitted in one direction (from browser to metrics server).

You could transmit the telemetry through Tor.

Tor is blocked in some places and viewed as very suspicious in others. If you're already in a place where you're trying not to draw attention to yourself, using Tor might not a good option.