Once you've saved a script, go to Plugins > NppExec > Advanced Options

At the bottom left, There is a section for adding Menu Items. Name your menu item something and select the script you want and click Add. Then restart Npp.

Now, if you go to Settings > Shortcut Mapper, you'll find your menu item in the list where you can give it whatever shortcut you'd like.

Sorry for replying to such a old post but I believe I have the plugin-less answer so I'll add it for historical and google indexing reasons.

What I did:
Create shortcut to Notepad++, opening Notepad++ by calling that shortcut from inside the shell.bat/cmd window. This will give it the fleeting PATH settings set in your shell.bat.

\"
"D:\Program Files (x86)\Notepad++\notepad++.exe" -nosession W:\Handmade\misc\HandmadeHeroNPpp.nps
\"
Here is what you can put in the shortcut path to also have a HandmadeHero Session file.
Added this here because the Notepad++ Wiki shows a way of opening with a session which does not work, You will need to manually save that session file (it will not be created if it doesn't exist, AFAIK) with this method you just need to configure NP++ to open .nps as Notepad++ Session files.
Like this: Preferences -> MISC.(tab) Lower right corner. write nps in the "Session file ext.:" window.


I then added the commend for build.bat in side NP++ via [Run] -> Run -> [...], then saved it to Alt + S.

When using Alt+S the window will disappear after the build is done but it gives enough time to see if there where errors at all. When I need the list of errors to persist I manually run build.bat in the shell.bat/cmd window.