GMail's "New Compose" doesn't support hotkeys since it has to allow for text entry.
There are however ways to use the keyboard to access the submenu as ashtu mentioned.
If you would like to label the message first before doing anything else, you can push shift tab to immediately jump to the drop down menu, then push space or arrow key up/down to expand the menu, then arrow up/down to label submenu, and then arrow right to expand to the label context menu.
If you were to label the message after writing the email, then it's a lot more cumbersome to navigate to that submenu using tabs.
In either case, it would likely be much more efficient to have a script to automate the tab presses.
In my opinion, a more efficient way to label would be to send the messages first, then navigate to the sent mail folder, and label the messages (in bulk) from there.