This depends almost entirely on what you're doing. If the site at issue isn't dynamic, my suggested action is probably "do nothing", because being frontpaged by HN is not going to tax any computer routinely used to serve web pages in 2017.

If you genuinely have problems, then the question boils down to "What is going to break first?" and whether it makes more sense to harden that or temporarily disable it. If you're a flight search engine and responding to flight searches is just intrinsically costly, then you probably need more capacity and/or a way to "shed load" and redirect folks into some sort of queue or alternative UX ("We're overloaded; give us your email address and we'll get back to you.")

If the dynamism on your pages is something that is incidental to their functionality, fakeable, or chosen simply for programmer convenience, you can dial down the dynamism for the time being via e.g. sticking a cache in front of the page, serving a static HTML version of it, pre-baking the default search/etc rather than recomputing it live for each of the 40k sessions, etc.

The most common "HN killed my website" is probably WordPress being served by Apache with KeepAlive on. That isn't simple to remediate if you continue serving WordPress from Apache; this would be one of my fairly few cases where it's a fundamental technology choice. (It is possible this has changed in recent years, but for a period of several years "apt-get php apache2" would get you an install guaranteed to blow up in production with over 10 simultaneous users.)