Finally, I’ve found the solution by myself.
There is a the_posts filter hook we have in the WordPress, which works after the system attempted to collect posts from a blog and, the most important, before defining the 404. Hooking it we can quickly update, or even modify, the array of posts, i.e. single post in my case, thus giving the system to continue working as nothing happened.
Due to that matter I’ve placed on the github the code of that tiny plugin and README with some explanations. If somebody will think that plugin should leave for the public audience, I would like to kindly ask to tell me about it, to continue development. Future ideas have been already placed in README.