How can we take a screenshot without typing the buttons?

Ways to Screenshot on Windows Without Print Screen:

1. Use Snip & Sketch or the Snipping Tool. Every modern version of Windows comes with a built-in screenshot utility called the Snipping Tool.
2. Install a Third-Party Screenshot App.
3. Remap Another Key to Print Screen.
4. Use the On-Screen Keyboard to Press PrtScn.

For the better understanding i have found some blogs you can refer to them:

https://www.makeuseof.com/tag/3-ways-to-screenshot-on-windows-10-without-print-screen/
https://geekbea.com/how-to-take-a-screenshot-on-dell-laptop/
https://www.pcmag.com/news/how-to-take-a-screenshot-on-any-device
https://www.91mobiles.com/hub/how-to-take-screenshot-on-laptop-windows-mac-os/

Unfortunately, there is no native way in Windows to take screenshot without pressing some keys.

If you use some screen capture program, it may possible to capture screenshot without pressing keys and with the help of cursor.

I don't know how to take a screenshot without the key button

Which "key button" ?

You can use the Game Bar Capture tool
([Win] + G to launch it or "Xbox Game Bar" from the Start Menu with the mouse, near the end of the programs list)

Try the snipping tool from the Start button.
Hope your mouse is working.