That wouldn't fly, turning off warp would instantly drop the speed. Theoretically, the ships are moving at very slow (non-relativistic) ship speeds inside the bubble. The only reason warp seems fast is because the space the ship's moving through is warped. If the space wasn't warped, the ship would just be moving normally. Theoretically anyway...

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Now if you want a low cost way to destroy a star, you have to learn from the real deal and use the star against itself. There are layers inside a star which are opaque and trap energy, if you can introduce elements to change the opacity of various layers you have a real shot at causing a change in the star's internal equilibrium using only a fraction of the stars mass in materials. If done rapidly enough and in the right places, this change could lead to a collapse and subsequent explosion (leaving behind either a neutron star or a black hole depending on the force of the collapse). In the very massive stars, if you can somehow trap enough energy in the core all at once, the opposite effect could occur, and the star could rapidly expand, resulting in an explosion that leaves no remnant.

Suffice it to say, the engineering involved in figuring out where, when, and how to affect opacity would be crazy hard since the inner layers are basically unobservable (especially after you've made them opaque). Complicating matters further is the fact that success in this endeavor would place you dangerously close to a supernova, wildly increasing your chances of imminent death, since by the time you can see it's exploding, you've already been exposed to way too much radiation. Who knows? Maybe there have been lots of successful attempts in the past... just with no survivors.

They opened a wormhole to a black hole and threw it into the sun. The black hole's gravity and time dilation held the gate open longer than normal and also sucked plasma through the opening and out of the sun. After enough matter was removed, the star's internal equilibrium between energy production (that pushes it out) and gravitation (that pulls it in) was disrupted to the point that the star built up an internal velocity inward. The result is typically an implosion shockwave and subsequent explosion of most of the star's outer layers as the shockwave rebounds. There would likely have been some kind of stellar remnant left behind, either a neutron star or a black hole (possibly even a still burning sun depending on the dynamics of the explosion). There's a few other ways a star could die, and they mostly depend on mass and composition.