Installing links or lynx (text-based browser) via entware might do it in some cases. Curl could also be used to post form information but it requires a bit more advanced knowledge / fiddling.
I see you run CE from SD card, so I guess that means you can still boot from internal to Android, right? Then you could also connect to the Wi-Fi in Android and then reboot to CE. The hotel Wi-Fi should remember the MAC address for a while and allow your box to reconnect without the login prompt. Just putting some options out there so you can find something that works for you.