SSIS is an application. You could have set the format in your package.
However, this is not the main concern: where is that package writing to? A file? A database?
If it's a database and you need a particular date format, that can only mean that you are storing the date as its human readable representation, which is not a good idea. You may want to read my article from 2012 on this topic: http://www.sqlservercentral.com/articles/T-SQL/88152/
If the target is a file, you should use an ISO format (such as ISO8601) rather than a nonstandard format.
So, going back to your initial question, maybe CONVERT with 100 style can do the trick right now, but it's probably contributing to a bad design. I have no desire to have the last word on this, I'm genuinely trying to help you, even if you don't seem to like it.
Also, remember that forums are not just for the OP, but also for other readers that may run into the same situation and seek for an answer, so pointing out the fallacies of dealing with date formats is not just in your best interest, but also in everybody's best interest.