We study optimal WMN routing using probing-based anypath forwarding, with explicit consideration of transient link uncertainties. Starting from a two-state link capacity model, we show the underlying connection between WMN routing and the classic Canadian Traveller Problem (CTP) . Inspired by a stochastic recoverable version of CTP (SRCTP), we develop an practical SRCTP-based online routing algorithm under link uncertainties. We study how dynamic next-hop selection can be done with low cost, and derive a systematic selection order for minimizing transmission delay. We further extend our solution to a general multi-rate link model, and present a Stopping Theory (ST) based solution, which naturally degrades to the SRCTP algorithm in the two-state link model. We conduct simulation studies to verify the effectiveness of the SRCTP and ST algorithms under diverse network configurations. In particular, compared to deterministic routing, reduction of end-to-end delay (51.15-73.02% for two-state links, 5.16% for multi-rate links) and improvement on packet delivery ratio (99.76% for two-state links, 94.44% for multi-rate links) are observed. By using RTS/CTS as the online probing tool in ns3 simulator, we observed both significant goodput improvements (29.9% than EXOR, 61.8% than HWMP) and much less packet arriving jitter (14.27 times less than EXOR, 45% less than HWMP) as compared to EXOR and HWMP routing protocols.