You can use a Chromecast on a WiFi hotspot, even without an active cellular data connection. I would expect a Cast-based screen mirroring utility to work, though not all apps will (and obviously not those that require an internet connection). The trick is to set up the Chromecast where you have a 'standard' WiFi network, then create your hotspot using the same configuration. The Chromecast should 'recognize' the hotspot and allow you to cast local media from your device (using Localcast, Plex, and such... though I haven't used these myself).
It's been a while since I've done this myself, so your mileage may vary, and I can't offer much specific advice as far as Miracast goes.