The Harris County District Attorney does offer first time offender the opportunity to apply for their pre-trial diversion program, as long as the offender meets their other criteria. The application will be reviewed by a specific prosecutor and either accepted or rejected. It seems to me to be a rather objective decision process. That said, if the evidence is strong against you, it might be a good program. It is a year long program with non-flexible terms. And the Judge presiding has no discretion in dealing with the program, other than an initial acceptance or rejection. The DA's office holds the power. If you are granted PTD and successfully compete it, you will most likely be eligible for an expunctions of the records of your arrest after a two year waiting period.
Since you are a first time offender, you can probably qualify for a Pre-trial intervention as the other attorneys have described. Your signed statement will not hinder your ability to get this, although they can try to use it against you if you wish to contest the charge. If you wish to apply for the program, they wil probably require that you write some kind of statement admitting guilt anyway. You sound like youre on the right track with your approach to this problem. Make sure you consult with an experienced criminal defense attorney.