It would surprise me if ldd supports mach-o and the darwin loader formats, and you seem to have demonstrated that it doesn't...
OTOH, lldb is generally built to support reading mach-o object files on linux, so you could use it.
The direct shared library dependencies are stored in the "load commands" of a mach-o binary, and lldb will read those. So just start up lldb, do target create
for your .app bundle, and image list
will show you the direct dependencies. lldb will recurse through all the direct dependencies to find the closure of the dependencies for that .app, but to do that you would have to have all the directly dependent libraries available (since their dependencies are in the "load commands" of the dependent libraries.) I'm not sure how you would get your hands on those.