I think you're putting the cart before the horse a bit here. The first thing I would do is come up with a list of the requirements you will be operating under due to policy, regulations, etc. It sounds like you need to have data encrypted at rest, and in flight, to start with, along with relatively fine-grained access control and significant capabilities for audit/logging of access.
Add to that whatever requirements you have for what authentication back end you want, editing capabilties, etc.
Then, with your requirements in hand, you can go looking for the right tool.
Maybe a wiki will work for some of it; you can use SSL with them, and most can be configured to only allow access to authenticated users. Wikis do track changes, which is good for auditing - careful use of the various access levels might go a long way towards building something decent with one. Where this approach is likely to fall down is in the fine-grained access control - in other words, making sure that only some people can see some stuff, and not other stuff. Wikis are generally not built with that in mind. Finally, I don't know of any wiki that handles encrypted datastores.
I might suggest trying to find some communities/lists that are specifically about HIPPA implementation. There may already be something you can use available, but just not commonly known outside of the communities that require it.