Hiked this four mile trail today from Allmendhubel to Mürren in misty afternoon. There is a detour around construction of a tower for a new lift to Schilthorn at the Suppenalp pension. It is narrow and steep for a half kilometer and in rainy weather like today, slippery mud. It was doable today but in a downpour, best avoided.
The steepness level of the detour is the same incline as the original trail - about 100 ft of gain in a quarter mile. The original trail is very very close to the detour, they just needed it to drive the construction vehicles on, so they added another walking path next to the original trail. Probably wouldn’t really be that fun of a hike in the pouring rain, regardless of the slight detour :)