Full-page-screenshot without third-party extension with Chrome

There are several extensions that will take a screenshot of the entire page, but the post demands no Chrome extensions.

A solution that uses instead the free key-remapping product AutoHotkey can remap some key for printing the entire Windows by simulating the sequence of keys described in the post.

The following AutoHotkey script will issue the above entire sequence when the F9 key is pressed:

F9::
Send, {F12}                        ; send F12
Sleep, 400                         ; wait for the developer tools window
Send, ^+P                          ; send ctrl+shift+P
Sleep, 400                         ; wait
Send, Capture full size screenshot ; send the command text
Sleep, 400                         ; wait
Send, {Enter}                      ; send the Enter key
Sleep, 2000                        ; wait while the page is generated
Send, {Enter}                      ; send Enter to store the image in default folder

If the waits (in milliseconds) are not long enough, then increase them.

After installing AutoHotKey, put the above text in a .ahk file and double-click it to test. You may stop the script by right-click on the green H icon in the traybar and choosing Exit. To have it run on login, place it in the Startup group at C:\Users\USER-NAME\AppData\Roaming\Microsoft\Windows\Start Menu\Programs\Startup.

Here is an answer on StackOverflow from a person working on the DevTools team who says it is not possible.

There are 2 comments to the original question regarding 2 issues created on the Chromium Bugs platform, you can track their progress to know when and if the features might be available -

1. Requesting the ability to customise existing keyboard shortcuts (#174309)
2. Specifically what this question wants - A keyboard shortcut to take a screenshot from DevTools (#743765)

So, this is definitely not possible natively inside Chrome, but can be made possible using third-party tools like AutoHotKey as mentioned in harrymc's answer or by using an extension like this one which the OP prohibits.