You have no say in the matter once you make your complaint to the police. It is up to the prosecutor whether to drop or go forward with charges
Listening to a lawyer who is not licensed in Texas who is "answering" a question of Texas law is not recommended. You have input in your husband's case, but it should be clear that you do not control the outcome. That is, you cannot just drop the charges. The State may eventually be persuaded that he did not in fact commit this crime. The problem for you is that "exaggerating" a story about a crime to the police is a criminal offense that you could be charged with. If you admit to the prosecutors or police that you lied at the time, they could charge you with an offense at that time or if you change your story when called to testify in court, you could be charged then. Your husband's lawyer may be able to convince them to dismiss the charge with your assistance, but I would suggest that you consider speaking to a local criminal defense attorney about the pitfalls of approaching the DA with the goal of correcting your story.
(Your husband could be revoked on the state jail and sentenced up to the max based on the time he received at sentencing. This is somewhere between 6 months and 2 years and must be served day-for-day with no good time credit. If he is convicted of a first time offense of assault-family violence that does not involved any alleged restriction of your airway by chocking, then he could face up to one year of additional county jail time or up to 2 years of probation.)
The victim services may be able to help you. Generally they are in close communication with the prosecutors. An affidavit of non-prosecution has successfully resolved a lot of my cases that were similar to yours. Although I always draft my own, I believe that the victim services also assists with these.