STL associative containers: erasing and getting back the (noncopyable) element

I am using STL associative containers (std::set and std::map) with keys which hold a std::unique_ptr<> instance. The key definition is equivalent to following:

struct Key
{
    std::unique_ptr<Object> object;
    bool operator== (const Key& rhs) const { return object->equal (*rhs.object); }
    bool operator<  (const Key& rhs) const { return object->less (*rhs.object); }
}

It is known that STL associative containers (esp. since C++11) do not have a way to obtain a non-const reference to the key to move from. And my keys are noncopyable, so c++: Remove element from container and get it back does not work.

Is there a non-UB way to overcome this problem?

My current solution is following:

template <typename T>
using map_pair_type = std::pair<typename T::key_type, typename T::mapped_type>;

template <typename T>
typename T::value_type take_set (T& container, typename T::iterator iterator)
{
    typename T::value_type result = std::move (const_cast<typename T::value_type&> (*iterator));
    container.erase (iterator);
    return result;
}

template <typename T>
map_pair_type<T> take_map (T& container, typename T::iterator iterator)
{
    map_pair_type<T> result {
        std::move (const_cast<typename T::key_type&> (iterator->first)),
        std::move (iterator->second)
    };
    container.erase (iterator);
    return result;
}