If I shut it down, not use it, never charge it, will there still be a risk of fire or something bad?
The key thing when you have a swollen battery is to keep as much energy out of it as possible. That means leave it dead, don’t charge it and try not to use it. That makes the job of whoever has to replace it somewhat less hazardous as well. Swollen batteries are a fire hazard despite some of the ridiculous comments in here. They only have a limited ability to deal with pressure and when they rupture, moisture gets in, reacts with the lithium and they catch fire. Also they are of increased risk of puncture when replacing them with the same outcome.
If this was an earlier model without the glued in batteries these are fairly safe to replace yourself. If it’s glued in, take it to a professional, preferably Apple.