What do you do if, despite your best efforts, you can't get a security policy written down? The safest answer is this: document, document, document. Write down what you're doing, and why, and what the existing policies are, and what you tried, and why you think the situation is bad. Print it out on paper, sign it, and deliver it - at least to your manager, if not to several managers above your manager. File a paper copy, with your signature and the dates you gave it to people.
Every year, or every time there is a significant change in the situation, try to get the policy created again. If it doesn't work, repeat the entire documentation process. Be sure to edit the document; it's tempting to just change the date and resend it, but it probably won't be quite right any more, and it weakens your position.
Doing what we recommend is fairly confrontational behavior, and it can look as if you're more interested in making certain that you're safe than in making certain your site is safe. It's worth working a long time on getting your document to say exactly what you want it to say. Don't fall into the trap of feeling that you have to use formal language. If what you want to say is "I understand that we're an informal company and we don't do written policies, but I think this issue is so important that we still need to have something written down," just say exactly that.