There are a couple of different issues here:
1. Due to the sheer number of public synonyms, it is true running the query and rendering the result in the navigator tree can be quite slow.
2. Attempts to cancel this long running task from within SQL Developer can fail.
A workaround to prevent yourself from accidentally running this task is to apply a (highly restrictive) filter on the Public Synonym node.
As for the cancellation issue, a bug was logged specifically for remote DB connections: Bug 12842181 - CANCEL ON PUBLIC SYNONYMS QUERY FOR REMOTE DB CAUSES HANG
but it might happen on a local DB also, either
A. As a true hang (probably due to using an incompatible JDBC driver version -- should be using ojdbc6.jar), or
B. As with the cancellation failing so that you must wait for the DB to return the query result.
Examples of (B):
* Windows platform limitation for Out of Bound Breaks, especially for SERVER=SHARED connections
* Perhaps you disabled JDBC Out of Band Breaks intentionally (as a workaround another issue) and forgot about it: Re: SQL Developer: Not able to view tables