upsie, I missed that bit - They also have to do it discreetly, (no violent explosions). yeah, probably have to delete this answer ....
it can even take a couple of years.
okay, now u made everything hard for everyone, and there are some interesting answers if we stay in sci-fy, but to add to the pool
what won't work
first of all, short on what won't work - adding matter on top of a star to change the ratio of elements to extinguish reaction won't work on timeframes of 100'000's of years. The reason for that is the core of a star, as matter does not move(mix) there that freely because of the density of it, and time mentioned is the time needed for energy to leave the core, so I guess it even worse for the matter to go in and redistribute. handwavium makes everything possible so keeping that in mind it can be a plot by itself.
Star dissassembler "Supernovae phuff 9000"
works in a similar way as to blow something to extinguish a fire.
There is such a thing as Muon-catalyzed fusion it makes fusion go faster mixing in particles which are similar to electrons by charge but more massive and when they orbit hydrogen it makes the effective size of such atom significantly smaller, thus improving reaction by kinda "reducing" repulsion force.
At least two pieces of handwavium needed - produce enough of muons and the second one to deliver them where they need to be, to the core.
The first one is lesser - energy produced by the star may suffice and as catalyst proportions, one does not necessarily need that many of them.
The second one probably as hard as mixing matter and complexity reduced just by 2-3-5 orders of magnitude because particles are smaller and fewer in numbers.
Getting to the core at concentrations 1 ppm or 1 ppb or 1 ppt or even in smaller cooncentratios they affect core bringing it to supernovae conditions, but u control the force or strength of its phuff by how much muons added in there.
Type Ia supernova produces about 1–2×1044 J in its blast, and for a star like sun u need something like 1/1000 of it, something on a scale of 2×1041 J or less as it about total binding energy of the star, but u need the stuff to stay in the system(so less energy) and just spit in chunks size of Jupiter, again less energy required overall.
A valid hole in the plot to be aware of is the question - if they have Muon-catalyzed fusion capabilities and are significantly more technologically advanced than the technology of today why not dismantle star directly. it is not clear cut and there can be many answers to it - why not, but it is indeed possible to be direct and dismantle a star, by as an example elevating the problem of delivering muons to the core directly and apply a pealing layer by layer approach in accordance of how deep in one can deliver those muons. or by throwing a few other legit(kinda) technologies to accompany the process and which can be stated conducted and managed by a small crew of people and not being them k1,k2,k3 civilizations by themselves. explanations are rather long and not clear but as it is related to those methods there are 2 relevant old answers of mine 1, 2 - so as u may look for other answers over there for inspirations and generally on wb as star engenering isn't a fresh topic here, mean a/q's do happen on that subject.
SG-1team accidentally sent a star heading towards destruction; the Asgard had to fix it for them. That's a form of acceptable handwavium. $\endgroup$