Be You Be You Be You Be You BE YOU.
These people will spend most of your waking life with you. If they don't want YOU, the real person, you don't want THEM, the uptight company.
The cover letter is obligatory, not because they want it, but because YOU need it to do anything other then be a set of keywords.
Talk about why you're a good fit for the role they're asking. Look at their company site and see what culture they claim to have, and write to it. Write how it will make you productive and encourage you to bring value.
Best of luck. If you become a startup guru, hire me, I'm hard working and a good lateral thinker...