Screen shot

You could try using Settings > Accessibility > Touch > Assistive Touch. Turn on the switch.

Then if you go into Customize Top Level Menu, you'll see all the configurations you can make.

I just played with it a bit..

You can have anywhere from 1-8 options/shortcuts which you can adjust with the +/- .

tap on the dashed box and it will bring up a list of different things that you can do with it. One of them is a screenshot.

This will show up as a small white dot on your screen at all times. If you have more than 1 icon, that white dot will open up a small menu/folder so you can choose from them. If you only set it up to have 1 icon, and you set that icon up to trigger a screenshot.. then pressing the white dot won't open a menu, it'll just do the screenshot