But do we have to cover the tagim of the nun?
I think you don't cover the tagim, and the tinok should be asked as seen here. Since, even if only because of the tagim of the Nun, they don't look like a mem, that is sufficient to machshir.
In regard to covering tagim in another example, we find in Mikdash M'at [32:60] in the name of Da'as Kedoshim, that a Yud that was a bit long and a tinok is asked if it isn't a Vav, the tag and oketz of Rabenu Tam must be covered, otherwise it's possible the tinok could not recognize the letter [Yud] itself, and only recognized it because of the tagim.
Below [right pic.] is a shayla on a long yud, and [left picture] after covering the tag and oiketz.
The Mikdash M'at doubts this, and paskens that b'dieved even if not covered, we accept the reading of the tinok.Seems to indicate that if we knew for sure, that the only reason the tinok recognizes the yud is because of the tag and oketz, his reading should not be accepted.
The Mishnat Hasofer (Yalkut Hasofer on p. 99) further doubts even this.
I think that even lachatchila the tag and oketz should not be covered - the correct way to ask a tinok is davka by showing the complete yud with tag and oketz, since these are correct parts of the letter. So, there is nothing wrong if the tinok would recognize the Yud only because these features.