Performance of query against column level dependencies much faster when using deprecated system view
I tried this rewrite that uses a temp table with the new DMF on AdventureWorks2014, and it runs around twice as fast as the version from your question.

SELECT t.[object_id], t.[name]
INTO #trigs
FROM sys.triggers t
WHERE 
    t.parent_class = 1 
    and t.is_ms_shipped = 0;

SELECT DISTINCT t.[name] 
FROM #trigs t
CROSS APPLY sys.dm_sql_referenced_entities
(
    'Person.' + object_name(t.[object_id]), 
    'object'
) deps
WHERE 
    deps.referenced_entity_Name = 'Person'
    and deps.referenced_minor_name = 'BusinessEntityID';


Here's a screenshot of the Plan Explorer summary after running both queries in the same batch (plans here):



The original query (the first row) runs for about 8 ms, the temp table version (the second two rows) varies between 4 and 5 ms.  Of course, your database might have vastly more triggers, objects, and dependencies than AW2014.

As Dan Guzman mentioned, you may also get some improvements by updating system table stats.



FYI - those two queries are not exactly equivalent.  The second query will not show the same results if there is a trigger in a different (non-dbo) schema that references dbo.JobVoyage.JV_VoyageFlight.  

In the example query from my test, there is a trigger in the Sales schema (iduSalesOrderDetail) that is returned by the deprecated view but not the DMF version, because the column I'm checking for is in the Person schema:



If all your objects are in "dbo" then this won't matter, but I thought it was worth pointing out.