Is there any way that I could add a button to NP++'s toolbar?
I have a shortcut which I use quite a lot. That would be nice if I could make a button out of it instead of pressing Alt+Ctrl+H each time.
There is a plugin "Customize Toolbar" on Plugin Central, or simply use Notepad++'s Plugin Manager. Its description says the plugin makes it possible that "buttons for Notepad++ or plugin menu commands can be defined using a configuration file." So it depends if your shortcut is a menu or plugin command. You could give this plugin a try.
You could also redefine the shortcut to something simpler, you only need to find and change the shortcut in the "Settings", "Shortcut mapper" dialog.