It's unlikely people will ditch their cars at a much faster rate than they are now, it's just that it won't be long til your average new car buyer changes preference to electric. Even when we get to the stage that most cars being sold are fully electric, we'll still have 50%+ ICE (internal combustion engine) cars on the road for some time, it'll be decades before they're mostly gone.
There's no reason to believe that people will start sending perfectly functioning cars to the wreckers en mass. By that stage, oil prices may have come down significantly, due to decreased demand, so it will likely be worth people's while to run their ICE vehicles into the ground before upgrading to electric. Secondhand ICE cars will likely get noticeably cheaper than they are now though because the market will factor in the running and servicing costs. Conversely, certain cars with classic, memorable engines will shoot up in price. I'm sure there's people starting to stockpile a few iconic V8s, V10s and V12s. Some of the high revving M3 straight 6s, classic WRX and Porches with their flat 4s and 6s, will do well too.
The recycling of car bodies is unlikely to make an enormous impact on iron/ore prices. When the rates for recycled steel are high, there's numerous ads in the paper, Gumtree, etc. with people offering to pick up scrap steel, car parts, car bodies, etc. for free because they can make money off it. When the rates drop, it's not worth the labour involved with stripping the bodies back to bare steel so you have to pay them to pick it up. So over-supply of car bodies has limitations to how far down it can drive the iron or price, many things are just too labour intensive to recycle and it can be cheaper to just dig it out of the ground.
You can retrofit electric engines to cars but it's prohibitively expensive if you are trying to come even close to matching the performance/range of anything offered by the car companies. You could easily spend in excess of $50k for the batteries alone.
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