First, you should call your auto insurance company and inquire as to what the repurcussions will be if you incur the points on your license as a result of the speeding ticket. Many insurance companies will give you a break for your first violation. If you currently have no points on your license and your auto insurance company will not surcharge you, it may be a good idea to go to court and get the charge reduced to a 2-point violation and then take the defensive driving course to have the points removed from your record.
Once you plead guilty to a traffic offense in Colorado it cannot subsequently be reduced or removed by taking any type of driving classes. That may be true in New Jersey. But not in Colorado unless it is part of the original plea bargain.
If you have a clean record it is always possible to get a zero point (non Moving) violation if you take either a 1 or 2 day defense driving class.
Best of Luck
A driving class is not an automatic point reduction, its just something that can be offered as quid pro quo for an amened charge with reduced points They don't have to keep the 2 point offer open either, so there is some risk in not paying the fine in advance. The odds of getting a ticket reduced depends heavily on your driving record, if you have any traffic citations in the last year, or have an otherwise bad record, then the 2 points is probably the best you can expect and it is riskier to not take the mail-in offer. With a clean record, a 1 point ticket might be negotiable, but zero point tickets are tough to get. The prosecutor you deal with usually has the discretion to decide what to offer, so who you get when you go to court can make all the difference.
Points cannot be reduced in Colorado once you accept a plea, so find out in advance if it will effect your insurance by calling your insurance company. If you have had any tickets in the last two years, be aware that accumulating 12 points within 12 months or 18 points within 24 months will result in your license being suspended (assuming you have an adult license).
You can always consult with an attorney about your case, there may be problems with it that could be used to negotiate a zero point ticket.