Could plastic or metal cans damage my oven?

You are taking me way back here. Back in my teens I used to do this as a fun project - I used Plexiglass (acrylic glass) instead of old vinyl records (people still used record players back then!), but the principle stays the same.

No, your oven won't suffer if you are careful.

• The metal can / bowl / heat-proof object underneath must be something that can withstand the heat. Yet 200F isn't that hot.
• Always put a sheet of parchment or foil between your tray/rack and the can/vinyl setup.
• Watch carefully. As soon as it shows signs of drooping / bending, take it out. You may always put your future bowl back in the oven to heat it more.
• It might stink, so make sure you have a window open and air out the oven afterwards.
  Do not try to bake cookies and this at the same time ;-)

Watch it like a hawk and open the door as soon as it's drooped. It's not a cake, so you can always shut the door again if it's not quite made it.

As @Stephie says, work on something disposable.

Plastic won't explode unless it's got an air bubble in it. Even then, any thermoplastic used in this sort of project (i.e. any plastic that melts in your oven) is likely to melt before the air gets too hot, and will pop gently. I'd be inclined to ventilate the oven well afterwards, and not cook immediately (you could acheive this by doing your craft project just after finishing cooking something, so long as the plastic doesn't smell).