I use "1Password" from Agilebits and it syncs with Dropbox without me having to sync with the desktop. For the initial setup, you may have to use their desktop application but I believe they have a free trial for the desktop, so you could just use it for the initial sync and then never have to worry about it after that. I use 1Password on the Mac & iPhone, but they both sync with dropbox and have no direct connection (although they do have that as an option) with each other.
http://agilebits.com/products/1Password/iPhone