Do NOT do that.
The chain goes along with the sprockets because the teeth are meshed perfectly when the chain is new, once stretched the teeth must deform to accommodate the chain, wearing the sprockets. When you use worn sprockets and a new chain suddenly very few teeth and only a small amount of material are contacting between the sprocket and chain, making everything stretch rapidly.
At minimum expect new crank, cam, and idler sprockets, as well as the timing chain tensioner and of course the chain. Do not forget the associated gaskets and fluids that will need to be changed. May want to also do the thermostat while you are there, and if you can the waterpump, hoses and belts.
Oh, and I would find a new mechanic.
His ideas are downright scary.