Can being free of publication charge be an indication of being a non-predatory journal? Though some serious journals charge publication fee as well, to a certain extent, can being free of publication charge be an indication,
albeit not a sure indication, 
of being a non-predatory journal? 

Since a less known journal suffers from being confused with a predatory one, if I want to make some of my publications free from being belittled, would declaring the journals publishing my papers are free of charge be a wise action?
No. A journal that does not charge publication fees can still be a predatory journal.

Generally, the motivation for publishing a predatory journal is to make money. Since the product they create (the journal) is too low in quality for them to be able to sell subscriptions and earn revenue from readers, they often make money by collecting publication fees from authors.

However, predatory journals may also have reasons not to charge publication fees. For example, when starting out, they may offer publication free of charge in order to get authors to submit to them, so they can build up a publishing history to look more legitimate. As another example, an individual might start a fake journal so that he and some of his friends have somewhere to "publish" (for career advancement), and accept submissions from other authors without fee so as to make the journal appear legitimate.