Webhook visibility for specific users only

I apologize in advance if this has been discussed before, or this question exposes my ignorance and unfamiliarity with integrations, but is it possible to set private visibility to the user who triggered a webhook in the same way that a slash command is only visible to the user who submit the request?

I want to be able to open a menu of options which is only visible to one user and depending on which option is selected, have a flask instance either send the response to the user originating the request, or the whole channel.