Sybase provides a utility called 'sybmigrate' to migrate databases automatically. I've never used it, but it may work well here.
If none of those work, you may look and see if Sybase Central can provide a table dump...
If you have PHP (or another host language) set up on either the client or the server you can run something like this (if you do not have too many tables and/or rows):
Of course, if you have many rows you can run into a PHP timeout. So you may wish to ORDER BY a unique column so that you can get a restart point.
$local = sybase_connect( "localhost", "sa", "not4u" );
$remote = sybase_connect( "remotebox", "sa", "alsoNot4u" );
$res = sybase_query( "SELECT col1
while( $row = sybase_fetch_array( $res ) )
sybase_query( "INSERT INTO myLocalTable VALUES ( " . $row[ 'col1' ] . ",
" . $row[ 'col2' ] . ")" );
} // end while