Is it really a problem to be a web application?
See: Node.js was made for the Web. Html5 is being developed to improve web applications. While Html5 is not totally equivalent to the potential of a well-designed Desktop application, it is sufficient for most cases.
I do not want to give an opinion here, I want to give a solution. Node.js is a platform for web development . If you do not want to use web, you can risk creating wrappers for GTK or WxWidgets, supported by C ++, for example. (If you do not know, Node.js natively supports C ++ add-ons)
Keep in mind that if you use Node.js, your application will be web. You can "pretend" that it is desktop for your clients, but in the background Node.js is web.
If your client does not have network access, you can create a package that installs and configures (if necessary) your Node application on your machine (or you can install it yourself if you do not want to venture out creating installers). Then creating a shortcut to open the browser in your application will be no problem.
If your client already has access and is willing to pay you for hosting, you can host your application on a server in the cloud. There are already good quality Node servers nowadays.
One last point: If you do not want to support all browsers (supporting all versions of IE has always been a problem), you do not need to. Ask the client to install a free browser such as Google Chrome or Firefox. That should not bother your client. All desktop applications depend on installer: management systems, office applications, games, even extensions to desktop applications depend on an installation. Why can not your application depend on one, too?