How to create a WebApi without Controller, only with DelegatingHandler?

Question

I'm trying to create a SelfHost WebApi 2.0 (not .net Core) for reverse proxy purposes. The api does not have any controller, instead I've created a DelegatingHandler that will proxy the request to some other place.

Here is the proxy handler

class ProxyHandler : DelegatingHandler
{
    protected async override Task<HttpResponseMessage> SendAsync(HttpRequestMessage request, CancellationToken cancellationToken)
    {
        return await RedirectRequest(request, cancellationToken).ConfigureAwait(false);
    }

    private async Task<HttpResponseMessage> RedirectRequest(HttpRequestMessage request, CancellationToken cancellationToken)
    {
        var redirectLocation = "http://localhost:8099";

        using (var client = new HttpClient())
        {
            using (var cloned = await CloneHttpRequestMessageAsync(request).ConfigureAwait(false))
            {
                cloned.RequestUri = new Uri($"{redirectLocation}{request.RequestUri.PathAndQuery}");
                return await client.SendAsync(cloned, cancellationToken).ConfigureAwait(false);
            }
        }
    }

    private async Task<HttpRequestMessage> CloneHttpRequestMessageAsync(HttpRequestMessage request)
    {
        var clone = new HttpRequestMessage(request.Method, request.RequestUri);

        if (request.Content != null)
        {
            var stream = new MemoryStream();
            await request.Content.CopyToAsync(stream).ConfigureAwait(false);
            stream.Position = 0;

            if ((stream.Length > 0 || request.Content.Headers.Any()) && clone.Method != HttpMethod.Get)
            {
                clone.Content = new StreamContent(stream);

                if (request.Content.Headers != null)
                    foreach (var h in request.Content.Headers)
                        clone.Content.Headers.Add(h.Key, h.Value);
            }
        }

        clone.Version = request.Version;

        foreach (var prop in request.Properties)
            clone.Properties.Add(prop);

        foreach (var header in request.Headers)
            clone.Headers.TryAddWithoutValidation(header.Key, header.Value);

        return clone;
    }

}

However, I couldn't make a "catch all" route in configuration, I've tried: config.MessageHandlers.Add(new ProxyHandler()); or

var handler = HttpClientFactory.CreatePipeline(new HttpClientHandler(), new[] { new ProxyHandler() });
config.Routes.MapHttpRoute("default", "{*path}", null, null, handler);

The ProxyHandler is called, however the client gets 404 http error: no route data was found for this request.

How can I create a configuration that doesn't need a controller and all requests goes to ProxyHandler?