java.nio.file.Path for URLs?

It seems like what you're really trying to do is accomplish what FTP does - copy files from one place to another. I would suggest you find better ways to do this with existing FTP code libraries.

URIs are not file system paths, so you can't treat them as such. They are addresses/resource locators that, when you go there with your browser (or another client that handles them), they trigger some action as defined by the server that's behind them. There's no standard for what that server does, hence the flexibility of web services. Therefore, if your server is doing to accept HTTP requests in this manner to facilitate file copies, you're going to have to roll your own, and pass the file data into a POST request.

To say it another way, (1) don't treat URIs like they are file system paths - they aren't, (2) find an FTP library to copy files, and/or (3) if you really want to build a web service that does this, abstract the details of the file copying via a POST request. If you do #3 understand that what your building is pretty close to custom, and that it will probably only work on a subset of sites that follow your particular design (i.e. the ones you build yourself). There's no standard set of parameters or "file copying" via POST command that I'm aware of that you can leverage to make this "just work" - you're going to have to match up your HTTP request with the web service on the server side.

You can do:

URI uri = new URI("http://www.example.com/foo/bar.html");
try (InputStream is = uri.toURL().openStream()) {
    // ...
}

It will work for http, https and file out of the box, probably for few more.

For relative URIs, you have to resolve them first:

URI relative = new URI("bar.html");
URI base = new URI("http://www.example.com/foo/");
URI absolute = base.resolve(relative);
System.out.println(absolute); // prints "http://www.example.com/foo/bar.html"

Now you can call toURL().openStream() on the absolute URI.