If the car has a tune in it already and you don't own the tuner that has the original Ford program with it then you need to get the car to a dealer to have them reprogram the car with the original Ford program. At that point then you might be able to pay HP to have one of your existing tuners reset/licensed to work with that Mustang. I believe this will render it unusable to tune with other vehicles unless you have it again reset. You'd have to contact HP to find out.
Note that if you have no cats then no tune will be able to compensate for that. No tuning adjustments are going to be available anymore to have deleted cats or to even mess with the O2 sensors. All tuning companies are now unable to allow for any kind of illegal modifications.
Unfortunately, a full exhaust isn't going to make much of a difference on a 3.8 v6 and the CAI by itself without any cam or head upgrade is not going to do anything at all. The CAI can only cause problems. It's a worthless part without major induction mods. I'm not talking about a TB or MAF either as they're also completely worthless without major induction mods.
Also, you aren't going to magically free up any noticeable hp. If you have an auto then you can adjust shift points to make a difference and you might be able to pic up just a very small amount of hp, like 5 hp if you're lucky, by making some adjustments but it's questionable to be worth the $ that HP will want to use their tuner with an Essex v6.