By far the best shorts for walking, are ones made by Salomon.
Their more designed for the distance trail runners, but are manufactured to very high standards, and are fairly long as well, so will provide good leg protection.
If you want high quality fully waterproof shorts, OMM manufacture some using their Gellanots fabric.
Their a bit on the pricey side, but like the Salomons, are high quality items, and both shorts are lightweight.