You can add a step that copies the template from some shared location into the expected local folder. Check the SQL Profiler Templates Missing - additional repair steps? for details.
The local folder depends on both the profiler's version as well as the version of the server you are connecting to.
For example, the SQL Server 2012 version of the profiler connecting to the SQL Server 2012 uses the following folder for templates:
C:\Program Files (x86)\Microsoft SQL Server\110\Tools\Profiler\Templates\Microsoft SQL Server\110