Essentially the standard / Radial / 4.7 are 3 different classes.
Most Grand Prix (open) meetings are sailed with 1 start and no handicaps applied, and prizes/results for different rigs are extrapolated from the overall placings. In this instance there is no obvious reason why you can't change down (or up) rig size, however you couldn't count your scores together for different rigs for the 'rig' results.
I know that the Laser master events 'allow' people to downsize rigs in order to keep people sailing when they otherwise wouldn't, but again you couldn't combine the rig results.
The Nationals (both the main summer, and the inlands) have 3 seperate starts for the seperate rigs. You would have to race in the correct fleet/start for the rig. Any results in the Radial would count in the Radial result along with any DNS's required to complete a series and likewise in the 4.7. I don't know if the race committee would simply allow you to change fleets (it is obviously an additional administrative task to amend start sheets midway though an event, especially if a lot of people do it). I don't know whether the organising committee would double charge you for entering both fleets!
It would be worthwhile you contacting the event organiser (listed on the Laser website) and asking directly. I'm sure that if you pre-enter the event and it is blowing old boots on the weekend, then you could elect to change without any penalty.
For what its worth, I think I could get a Radial round a course in a F5-6 just as quick (if not quicker) than a standard rig with less chance of an unforced error (i.e. swim at the gybe mark), so it sometimes pays to go smaller!
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