Recently had to do this. I ended up using pointers...
Quick Benchmark Results
#include <iostream>
#include <type_traits>
#include <algorithm>
#include <map>
#include <vector>
using map_t = std::map<int,int>;
const map_t m
{
    { 5, 20 },
    { -18, 28 },
    { 24, 49 },
    { 17, 27 },
    { 23, 46 },
    { 8, 16 },
    { -13, 11 },
    { -22, 32 },
    { 12, 45 },
    { -2, 19 },
    { 21, 11 },
    { -12, 25 },
    { -20, 8 },
    { 0, 29 },
    { -5, 20 },
    { 13, 26 },
    { 1, 27 },
    { -14, 3 },
    { 19, 47 },
    { -15, 17 },
    { 16, 1 },
    { -17, 50 },
    { -6, 40 },
    { 15, 24 },
    { 9, 10 }
};
template<typename T>
void sort_values_using_vector(T const& m)
{
    using map_t = T;
    using sort_t = std::vector<std::pair<typename map_t::key_type,
        typename map_t::mapped_type>>;
    sort_t sorted{ m.begin(), m.end() };
    
    std::sort(sorted.begin(), sorted.end(),
        [](auto const& lhs, auto const& rhs)
        {
            return lhs.second < rhs.second;
        });
}
template<typename T>
void sort_values_using_multimap(T const& m)
{
    using map_t = T;
    using sort_t = std::multimap<typename map_t::mapped_type,
        typename map_t::key_type>;
    sort_t sorted;
    for (auto const& kv : m)
    {
        sorted.insert(std::make_pair(kv.second, kv.first));
    }
}
template<typename T>
void sort_values_using_ptrs(T const& m)
{
    using map_t = T;
    using ptr_t = std::add_pointer_t
        <std::add_const_t<typename map_t::value_type>>;
    using sort_t = std::vector<ptr_t>;
    sort_t sorted;
    sorted.reserve(m.size());
    for (auto const& kv : m)
    {
        sorted.push_back(std::addressof(kv));
    }
    std::sort(sorted.begin(), sorted.end(),
        [](auto const& lhs, auto const& rhs)
        {
            return lhs->second < rhs->second;
        });
}
template<typename T>
void sort_values_using_refs(T const& m)
{
    using map_t = T;
    using ref_t = std::reference_wrapper
        <std::add_const_t<typename map_t::value_type>>;
    using sort_t = std::vector<ref_t>;
    sort_t sorted{ m.begin(), m.end() };
    std::sort(sorted.begin(), sorted.end(),
        [](auto const& lhs, auto const& rhs)
        {
            return lhs.get().second < rhs.get().second;
        });
}
static void copy_to_vector(benchmark::State& state) {
  // Code inside this loop is measured repeatedly
  for (auto _ : state) {
    sort_values_using_vector(m);
  }
}
BENCHMARK(copy_to_vector);
static void copy_flipped_to_multimap(benchmark::State& state) {
  // Code inside this loop is measured repeatedly
  for (auto _ : state) {
    sort_values_using_multimap(m);
  }
}
BENCHMARK(copy_flipped_to_multimap);
static void copy_ptrs_to_vector(benchmark::State& state) {
  // Code inside this loop is measured repeatedly
  for (auto _ : state) {
    sort_values_using_ptrs(m);
  }
}
BENCHMARK(copy_ptrs_to_vector);
static void use_refs_in_vector(benchmark::State& state) {
  // Code inside this loop is measured repeatedly
  for (auto _ : state) {
    sort_values_using_refs(m);
  }
}
BENCHMARK(use_refs_in_vector);