No, sorry. Webscorer timestamps everything as it comes in, and not even I can adjust those timestamps.
Personally, I always run without my phone and record on my Garmin, so please don’t feel the need to run with a phone if you don’t like to. I just enter my run in Webscorer as soon as I get back to the car. The main problem with using the phone to scan the course QR codes is that it will add some time as you fiddle with your phone at the start and end. Of course, you can always edit the scanned time to match with what you record on your watch.
The only downside of manual entries is that they introduce human error, in not recording immediately, in choosing the wrong course (not possible when scanning), or in entering the time wrong. None of these are major issues, and the vast majority of manual runs are being submitted correctly. If you do have problems, see: