Are there any third party tools that can read and/or analyze SQL Profiler trace (.trc) files
I would probably import the trace to a table, for example:

USE MyDB
GO 
SELECT * INTO MyTraceTable FROM ::fn_trace_gettable('C:\Path\To\My\Trace\MyTrace.trc',    
DEFAULT)


If you don't have permissions to create a table, consider using a temporary table or installing SQL Server Express locally and importing the trace there.

Kin's answer (entered concurrently with mine) might be a better option, but I haven't tried ClearTrace yet.