Template parameter dependant [[nodiscard]]

You can use SFINAE to select between two overloaded operator (): one of them returning void, and another one for the rest of cases annotated with the [[nodiscard]] attribute:

#include <type_traits>
#include <iostream>

template <typename FuncT>
class Wrapper
{
    private:
        FuncT funcToWrap;

    public:
        Wrapper(FuncT ftw) : funcToWrap(ftw) {}

        template <typename ...ARG, typename T = std::invoke_result_t<FuncT, ARG...>>
        std::enable_if_t<std::is_void_v<T>> operator()(ARG&&... args) {
            std::cout << "Test 1" << std::endl;
            return funcToWrap(std::forward<ARG>(args)...);
        }

        template <typename ...ARG, typename T = std::invoke_result_t<FuncT, ARG...>>
        [[nodiscard]] std::enable_if_t<!std::is_void_v<T>, T> operator()(ARG&&... args) {
            std::cout << "Test 2" << std::endl;
            return funcToWrap(std::forward<ARG>(args)...);
        }
};

int main() {
    auto testfunc1 = [] { };
    Wrapper test1{testfunc1};
    test1(); // <-- No warnings should be issued here

    auto testfunc2 = [] { return 0; };
    Wrapper test2{testfunc2};
    test2(); // <-- Warning issued here
}