Hello,
I'm with bend, don't think the lack of a cone has any relevance.
If you are looking to have the charge reduced, Early Resolution is an option for you. It is likely that a lesser charge will be offered for a plea of guilty. Highly unlikely the charge will be withdrawn, or that you will have any opportunity to express any opinion as to why it should be through Early Resolution.
To defend against the charge, I recommend seeking professional representation; once you go to trial it is all or nothing, and a Careless conviction usually means very expensive insurance rates (and a license suspension for any G1 or G2 driver under escalating sanctions).
Another option at this time would be to ask for a trial, very frequently a plea deal is offered before the trial would begin. If you choose early resolution, and don't like the deal, you can then request a trial as well.
Think about submitting your ticket, and requesting disclosure. Once you see the evidence against you, you can take it to a representative (lawyer or paralegal) for an opinion on how to proceed.