That would be prone to abuse (any website could just launch native applications).
You can create an extension that exposes a URL, say, chrome-extension://extension-ID/launch-application. This page will accept query string parameters, for example, ?name=Word.
Note - It should make sure that the referrer is empty (in order to make sure the user clicked on a bookmark and not a website navigated to this URL, though I am not sure this check is very secure, you might be able to use a service worker in your extension and make sure the sec-fetch-site is none, if that is accessible).
The page can then use native messaging to tell a locally installed native application (should be installed on a computer along with the extension) to launch the relevant application.
Note - why a ?name=Word and not a ?path=path/to/winword.exe? To narrow the attack surface, in case someone manages to spoof the request from a website and cause harm to the user. You create an allow-list in your extension and in your native messaging host, which is a minimal and basic protection against arbitrary launches.
It would be nice to also have some user-unique salted hash in the URL that should be passed to and get verified by the native messaging host, which provides another defense against arbitrary activation.
I imagine/realise this is a bit more than you had hoped, but this kind of feature can be a can of worms you do not want to open so easily.