RouterOS’s container feature doesn’t run on MIPS devices today and likely never will.
SSH over Cgi request: cool, but it needs an external server (ok, it’s available), an active internet connection, a public IP, expose port 22 to interent, Interesting but not the best way.
There’s nothing about web apps that requires them to be hosted on a public server for use “inside the LAN,” as you qualified your initial question. In fact, going out to a public server and then back in merely to provide a one-button reboot service implies so many security risks I don’t even want to try listing them all here.
So fine, containers won’t run on your MIPS based router, but they will run on every other x86 and ARM-based host on the LAN. There’s also virtual machine tech, if you don’t mind the bloat of installing a whole other OS atop another.
Surely you have something else on the LAN besides the router that’s up all the time and has enough free resources to run a container or a VM in the background. A PC that stays up all the time? The Mac Mini in the closet that serves the iTunes library? The NAS?
I have android, I need an app for that. Or maybe you have a suggestion?
I haven’t been a daily Android user in many years now, but a quick search of the Play Store turns up a whole pile of SSH clients.
That having been said, what’s wrong with using one of the available MikroTik apps for this? I got the official “MikroTik Home” app running on my ChromeBook, and it’ll reboot the router with a few clicks: More → System Settings → Restart → Yes. It isn’t a single big red button, but it is pretty easy.