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One of our writing group initially objected to Chewbacca's complaint that it's implausible to blow up a moon with hand-portable explosives. He suggested that you could probably carry enough antimatter to blow up a moon.
The gravitational binding energy of Earth's moon is about 1029 joules. This means that to blow up the moon, scattering its particles just fast enough that they can't collapse and reform under its own gravity, then we need to deliver that much energy. Using good old Einstein, E = mc2, we can generate this much energy by annihilating just over 1 trillion kilograms of mass. If we do it by a matter-antimatter explosion, we need half this much antimatter (the corresponding amount of matter can be taken from the moon itself), or 500 million tonnes of antimatter. So not exactly something that Chewbacca could reasonably be carrying in his backpack.
In canon, the forest moon of Endor is actually slightly bigger than our moon, at 4900 km diameter, compared to 3475 km for our own moon. However there is no canonical source for the mass or density of the forest moon. (People have tried to calculate it using shots from the film, but the numbers come out inconsistent and unrealistic.) But given the binding energy goes up as the fifth power of the radius (for constant density), it's going to be somewhere in the order of 5 times that of our moon. So the amount of antimatter you need will be somewhere around 5 times as that quoted above. And it's plausible that the forest moon would also be slightly denser than our moon, which would add more.
Of course you may not want to blow the entire moon to smithereens. It may be enough to disable some critical systems so that the giant weapon won't work any more. But where's the fun in that?
Commentary by memnarch (who has not seen the movie)
Ben seems to have forgotten that it was the experimental hyperdrive modulator that let only them get inside the shield in the first place. And even discounting that, there had to be a reason that not all of the ships made the jump. Blowing up the shield generator controls to turn them off sounds perfectly reasonable to me; there's even a comic that points this out as a viable method as well! It's highly unlikely that either part is pointed out in the movie like this though, especially since the shield was simply turned off from a console and said console wasn't blown up immediately afterwards.
Perhaps the original movie plan was to take the shield down and then the Resistance fleet destroys the base while the main characters rescue Rey before fleeing? And now that the space attack is obviously not going to succeed with its part, it's time to just destroy the controls for the base to buy more time. It's seemed unlikely that we'd end with exploding the whole moon by direct attack for a while now, so disabling the firing mechanism so the paradox shot goes wrong or the refueling doesn't stop or something that makes the station blow itself up, even partially, feels like a sensible way to end the movie.
Transcript
[SFX]: Pow! Pow!
Finn: Looks like they’re in trouble. They’re not going to be able to destroy the Peace Moon. We can’t leave.
[SFX]: Pow!
Rey: What do you propose?
[SFX]: Boom!
Zeppo: I’ve got an idea!
Zeppo: Chewie, you still got those explosives?
Chewbacca: Have you seen us blow up anything yet?
Zeppo: We find a weak spot and use them to blow up the Peace Moon!
Chewbacca: Hand-portable explosives to blow up an entire moon? If that were remotely plausible, why was that not our plan in the first place?
Zeppo: We were going to use them to take the shield down.
Chewbacca: But... we had to get inside the shield to do that anyway.
Zeppo: Every plan should have an even better back-up plan!
Rey: To be fair, it is better than his first plan.