If you have to go to the post office to mail the application, why don't you just buy a money order there and send your application in a manner that you can track it to be sure it was delivered.
I have always sent payments for guns, gun permits, or any other type of applications having to do with firearms via overnight mail. I want to know when the clock should start ticking on timed items.
Since you have to go to the post office anyway, why not just get it there?