This way of reciting the mantra japa [i.e. ṣaṭcakrajapa] with the location of the bījākṣaras in the proper places in the body is called a nyāsa vidhi. Nyāsa means a placement of the bījākṣaras in their proper places. This method gives you quick results and therefore this method is recommended.
In case you are not able to recite it this way, with the nyāsa, you may recite it simply. The recitation must be purely mental. There must be no sound coming out of the lips. There must be no movement of the lips. There must be no movement of the tongue. The mantra should be recited internally in the mind. And the mind's ear, not the external ear, listens to that mantra. So this is the procedure for the mantra japa.
Of course, in order to get to know the rhythm of the bījākṣaras, and the way they are to be pronounced, you may, in the beginning, recite the mantra outside. But then, you must, as quickly as possible, once you've got them by heart, you must internalize them, and you must learn to sing these mantras, which are the names of the gods, inside your mind, and you must be able to listen to them mentally.
When you are able to do that, you can do the mantra japa at any place, at any time, without any consideration whatsoever for your state of purity. I am saying this because, in some cases, the woman may have the menstrual periods. During this time also, they can go ahead with the internal mantra japam. Or some people may have the doubts, like when you are going out, you are talking with people, or you are mixing with people in various ways. At that time also, the mantra japam can always be done internally.
If you are reciting the mantra externally, then, of course, there are certain demands on the state of purity of the individual. But for internal japam, there are no restrictions whatsoever.