To take advantage of the
TiddlyWeb features you need to be able to run a server of some sort. It is possible to build things so the server is running off a shared disk. If you just want a
TiddlyWiki itself, it can be loaded from a shared drive, as an HTML file, but there are issues with locking for edits. There are plugins that can deal with that. See
http://tiddlywiki.org/