Once an incident has been reported, and a charge filed, there is little a "victim" can do. This can be very frustrating for a victim like you who does not feel threatened, and who may have been a mutual aggressor. Unfortunately, it is out of your hands. It is up to the prosecutor whether or not they will continue forward.
There are a few different things that can happen.
1- the charge will be prosecuted anyway. A lot of times, prosecutors will view uncooperative victims as being afraid due to repeated abuse. Recanting happens a lot. The prosecutor will go forward with the charge anyway.
2- the matter will be set for trial and depending on whether or not the prosecutor believes they will prevail at trial without a cooperative victim, the matter may go to trial, be resolved, or dismissed.
3- the prosecutor will take a look at the history between the parties and of the individual charged and make an offer to negotiate the charge.
What you can do, is get a hold of the victim's advocate. It is their job to speak with you and then relay your concerns to the prosecutor and Court. If you have no safety concerns, let them know that.
Bottom line is you, have no control over the charge being dropped.
As far as the no contact order goes, it is a Court order and violations are taken very seriously. It is hard for two parties who have a no contact order and who want to be together to abide by the order. It is so easy to violate the order, but any violation will make things much, much worse for your boyfriend. The third violation can be charged as a felony.
It is important that your boyfriend go through the proper steps to motion the court to have the no contact order recalled. You cannot ask the court to have the order dropped. It has to be the defendant. What you can do is make sure the advocate knows how you feel. This way, they can inform the Court of your wishes.
It is always beneficial for a defendant to have an attorney with him to advocate for the recall of the order.