1. The Prince of Wales becomes King the moment the Queen dies.
2. The Princess of Wales, unless divorced, becomes Queen equally automatically.
3. The Prince becomes Supreme Governor of the Church of England by virtue of his accession. This is a statutory office.
4. A coronation affects none of these things.
Since in the present circumstances a coronation of King and Queen would be absurd, cut it out. That would spoil the fun of the tourist industry but have no other effect. Many English sovereigns have not been crowned.