I think I would move it into a separate namespace
namespace tricks {
using std::swap;
template <typename T, typename U>
void swap(T &t, U &u) noexcept(noexcept(swap(t, u)));
}
template <typename T>
void swap(my_template<T>& x, my_template<T>& y)
noexcept(noexcept(tricks::swap(std::declval<T>(), std::declval<T>())))
{
using std::swap;
swap(x.something_that_is_a_T, y.something_that_is_a_T);
}
Alternatively you can move the whole code up into tricks
and delegate to there.