Disintegration is a fantastic suggestion. It ensures that the weapons platform that you just spent billions of dollars building can’t be reverse engineered or interrogated if it’s captured. Also, it makes a pretty solid failsafe, should it go rogue and turn against you… wait, you meant disintegrating other things, didn’t you? Well, this is awkward.
Let’s just get the combat training out of the way, your character will be trained in whatever they knew from the military. That can be whichever hand to hand set is most appropriate. Just remember, their combat training will have them using firearms, and this isn’t something they’ll just ignore.
So, here’s the thing. You, as the military, spend fifty billion dollars building a better soldier. Obviously, that kind of cost is not going to fly on a mass rollout, and the modern military is all about mass production, but, for the moment, your prototype cost a lot of money to research and build. You do not want to lose that money. You don’t want another faction simply scooping your prototype up off the street, hauling them off to the dark side of the moon, and taking them apart to figure out how they work. So, you’re going to need failsafe systems.
One of the easiest ones is GPS tracking, along with a communications package. This means, wherever your prototype goes, you can always call it up, and know exactly where it is and what it’s doing. For something like this to actually work it cannot be something the character can just switch off whenever they want. They’ve got a radio in their skeletal structure now, and like it or not, they can’t do anything about that.
More aggressive failsafes will probably be prudent. No matter how good your psychological screenings are, there’s always a chance you’re giving someone limitless power, and they’re just going to take off and start murdering their way through the government. That means you (still, as the military) need to be able to, at least, shut down their enhancements, if not outright kill them remotely.
This brings us back to the disintegration option. If your prototype is captured by some organization that wants to reverse engineer your technology, you need a way to stop them remotely. Also, if you’re doing clandestine things with your prototype, it’s always nice to have an “I don’t know what you’re talking about. You’re evidence melted? That’s preposterous!” out, if they’re captured.
I say “melt,” rather than “evaporated”, because, for the most part, setting nanites to break everything in their general vicinity, is believed to result in a grayish sludge, though they could be set to incinerate anything around them, so it’s all up to your preferences.
Okay, now, what else can they do? Nanotech is fairly fluid, at least in science fiction, so there isn’t really a shortage of options. The Crysis and Deus Ex (except Human Revolution) games both feature nanotech augmented player characters, so those might be worth looking at. Crysis 2 in particular does spend some time poking at the plausible applications for the technology, so if you have the time and aptitude for first person shooters, it’s probably worth looking at. Also, it will get you thinking about (relatively) realistic firefights with superpowers.
What superpowers your character gets are ultimately up to you. I’d actually recommend against areal dispersion, though. Nanites are just tiny robots, so they need a medium to traverse, that can be a human body, water, solid surfaces. But, throwing them in the air is more weapon-of-mass-destruction territory than a superpower.
Some fun possible superpowers are cloaking, limited shapeshifting (can’t change size, or gender), rapid healing, improved resistance to damage (armor or improved pain resistance), heightened reflexes, improved strength. You know, the usual super power set. Your character might be able to interact with nearby electronics if they infest them with their own nanocolony first. Though, that would mean they’re depleting their own reserve of nanites.
On the supervillian side of things, nanites could be used to control individuals, Star Trek’s Borg Collective and the 2009 GI Joe film both have examples of that. This isn’t a good option for a military with loyal disciplined soldiers, but, for a supervillian who needs stormtroopers for their volcanic fortress, it’s a possibility.
I mentioned psychological screening earlier, here’s the thing, unless the entire point of the experiment is only for rapid healing, then picking a critically injured soldier is probably a poor choice. The reason is fairly simple. You need to run extensive psychological screening for any kind of prototype technology, before integrating it. So you don’t stick it in someone that will immediately pull a Robocop 2. Any traumatic injury runs the risk of psychologically destabilizing the patient. I don’t mean they go insane, but things like depression, anger, obsessive tendencies, hell, even PTSD are all things you DO NOT WANT, when you’re trying to test out some new high end cybernetics. If these do emerge, you’re going to be left asking if it was the result of the injury or if it was the result of the implants.
The major exception is if her nanotech infusion was only to speed her healing. Obviously, this is wandering off the entire super soldier concept, but, then the only thing she’d gain would be the ability to heal from egregious injuries (possibly including death) quickly. In a situation like that, you might not need anything beyond the infusion. Including failsafes. To be honest, if that’s your character’s only superpower, that’s probably enough, provided they’re creative. Also, I find it stresses credibility a little that the military would pick someone for this treatment, if there was the slightest risk of them just taking off after treatment.