There is a router and there is a tablet for Android. They are connected via Wi-Fi.
what method can I use to disable the router remotely from a tablet?
I need a simple way. immediately launch or tap the program or icon on your tablet a couple of times.
I can’t grant full access from my tablet to the router. I don’t trust the tablet much.
what are the simple options for shutdown?
Port knocking is one or using the TikApp with reduced privileges.
You could also create a specific WEB SKIN (see SKIN design) that has only Shutdown option.
Port knocking is probably the best if its really a “one press” action you want
and at same time you do not want someone to actually connect to the router.
Connect a power-plug (Zwave/Zigbee/Wifi) between router and outlet on the wall.
Note this is not really a “clean” shutdown 
Not sure if that could be problem. It would more be in a panic/kill-switch situation.
This is also the only way to ACTIVATE the router again. If you choose “shutdown” you cannot ever remotely send any command to the router to wake it up again and you need to remove/apply power again.
What is your exact “use-case” for this ?
I thought to use the knock on the port. this is really the easiest and safest way.
I just thought there might be another way, but it looks like it’s not there.
Most, even basic, routers have a feature called remote management. When that is turned on & its access credentials configured, you can login to your ‘online’ router practically from anywhere provided you’re also online. From there you can pretty much do anything like disable its WiFi broadcast, change its password, change SSID (WiFi name), reboot or even shut it down. Anything.
If that fails, or seems very complex, just leave your PC or laptop on, then have a remote access software like TeamViewer installed. With that you can, more or less same way as above, access your PC then type in the gateway/router IP in the address bar and you’re into the routers console.
Those two scenarios work well for me especially when it comes to monitoring bandwidth usage and applying control metrics for my remote clients. I hope this helps.