As the US document from 2000 linked to above indicates, the current status of the Scapular Confraternity is a bit messy (as in disorganised), especially, apparently, in North America. Even that document, though, does include being invested in the scapular on its list of gradations, and refers to the
1996 document approved by the Holy See as the latest version of the rules. I am not aware of any subsequent rules since then.
Therefore, you do not need permission to substitute the rosary or another part of the office for the Little Office to share in the benefits of the confraternity, since it explicitly lists these “or other equivalent prayers” as appropriate. (Though I suppose if you had a question about whether some other particular daily devotion should qualify as “another equivalent prayer” that might be something to check with a Carmelite or a priest with.)
Your other question I would rephrase as “what happens if I
don’t do the prayers?” In that I agree with the other posters that, like the Rosary Confraternity (which I’m also a member of), you commit no sin, but you do lose the benefits, until such time as you take up the prayer obligation again.
But even then, many of the benefits of wearing the scapular accrue to those who practice its spirituality whether or not they are invested (though I would submit that daily prayer is a pretty fundamental part of practising Carmelite spirituality!).
The biggest objective advantage that being invested offers, based on my reading of these two documents, is the eight plenary indulgences that are available to those invested in the confraternity (under the usual conditions). [NB by ‘objective’ I mean having official status in the Church–I’m not presuming to interpret private revelations relating to the scapular, and still less to foist my interpretation on others.]
(Subjectively, I find that being invested also offers encouragement to the wearer to perservere, and gives a form and structure in which one can live one’s spirituality, while still not being as big of a commitment as joining a third order.)