The one they give also crosses numerous rivers and lakes. For the strict version of the challenge where you literally can't cross water it's likely that the best solution is across Antarctica. Guaranteed by temperature to contain no water whatsoever.

> Guaranteed by temperature to contain no water whatsoever.

Depends on where and when.

Plenty of puddles form around the bases in summer.

I'm confident that the Land Paths need bridges to cross the numerous rivers along the route. You need a different qualifier.