Constitutionally, that would be Kamala, in the event it's a known thing that the sitting POTUS has stepped aside to medically recover from something. (But we all here know [DS] doesn't follow the Constitution at all, so it's anyone's guess as to who is really calling the shots militarily.)
However, DOD has some unilateral power in where it's forces go and for what reasons, as long as it isn't on any official war footing/capacity. If it's in the name of defense of freedom of navigation treaties, or as a show of force, or peace time training of, for, or with foreign ally forces or prospective ally forces, or for anti-drug/anti-Cartel ops while embedded with DEA, or just normal deployments, then it's fine. POTUS doesn't have to always approve tasking orders. I'm fact, most of the time POTUS wouldn't even be made aware of where all our forces are, or where they're deploying to, or what they're even doing, at any given time.
As for "nuclear forces" being deployed, our CBGs (Carrier Battle Groups) technically, and/or officially haven't carried nuclear weapons onboard in quite a while now. Decades, in fact. The use of the phrase "nuclear forces" is wrong in the context given by "Colonel Towner-Watkins." Just about every USS ship we have are "nuclear powered," and would constitute the use of the phrase "nuclear forces," but that isn't how it's used in the military. The true meaning of "nuclear forces" while used in strategic/tactical ops planning is only used in a weapons platform context, meaning "nuclear capable forces," or "nuclear equipped forces." And this "Colonel" should know that, if this person is, in fact a Colonel.
Constitutionally, that would be Kamala. However, DOD has some unilateral power in where it's forces go and for what reasons, as long as it isn't on any official war footing/capacity. If it's in the name of defense of freedom of navigation treaties, then it's fine. POTUS doesn't have to always approve tasking orders. I'm fact, most of the time POTUS wouldn't even be made aware of where all our forces are, or where they're deploying to, or what they're even doing, at any given time.