Is there a shortcut key for the cloak?

In the main menu, go to:

• Options
  • Customize controls

All the keybindings are there. Cloaking defaults to c.

You can always listen/watch for weapon/missile launch sounds/animations, hit the Space bar (it's your friend, use it and abuse it often) or middle mouse button (added in version 1.03.1) to pause, and toggle the Cloak and/or trigger it's respective hot key (added in version 1.03.1, customizable in the options menu).

As of this comment, I believe you can only use the number keys to select a weapon and fire (and to activate drones).

1 2 3 4 keys, depending on how many weapon slots (e.g., weapon slot 1 = 1 key).

The 5 6 7 keys to your drone slot (as mentioned by Joe Wresching, and depending on the amount of drone slots your ship has).

Unfortunately, since you also use those same keys to select a dialog option, it can cause you to "accidentally" surrender. You can turn off these shortcuts off in Options.

In version 1.03.1 (added Dec. 21 2012), hot keys added for many actions (including cloaking), and is customizable from within the Options menu. Cloaking will also automatically cool down when your ship is out of danger and you can now also use the middle mouse button to pause the game.