>>>Can I not say it's in the post?
If you were unlucky enough to get caught for not having a tax disc, it would almost certainly be because an ANPR camera had examined the DVLA database and discovered that you'd not paid for a new disc, rather than through a police officer actually looking at your windscreen. So it would be no good saying that it was in the post because it would be obvious that it couldn't be.
I'd probably chance it but , if you want to be safe, drive to the dealership on 31st August and leave your car there. Take a bus or taxi home (or get a lift or simply get fit and walk!) and do the same the following morning.