If we can do what Birdie said, then do that.

Otherwise, get Shuri to leg it for the cave. The best route is probably to follow the pipe to Y3, then circle round to the right. When she reaches AE3/E3, follow the pipe south to the glowing light at D10. She can pause there to warm back up, and also check on L33tz4n.

That's probably not the shortest possible route, but a) it's reasonably short and b) it has landmarks. Feel free to adjust it slightly for the actual scale of the map.