Yes, AFAIK it is not possible : EXP can be used to export only tables, or only grants, or only indexes, BUT it don´t give to us an option to export only synonyms.
The best way to "pass" only the synonyms to another db is to create a scrit with the necessary CREATE SYNONYM in sql*plus, selecting the data from DBA_SYNONYMS or ALL_SYNONYMS, as desired.
Another option (not preferred due to mount of work) is extract the CREATE SYNONYMS from an exported file.