I've updated my comments on Nymeria's wheel. Since you get 20 durability from 8 stacks it means you only need two good/exclenent procs for whistle to be efficient. Getting one satisfaction procs and Nymeria's wheel +20 durability (8 stacks or lower) is the minimum needed to justify the use of whistling (vs CP costs).

What this means is specialist whistling will almost always be efficient with the proposed cycle. Note though, trained hand will be hard to fit in all the time, it definitely requires a CP surplus.