@TivoliHA will do - I'll send you a DM.
Shyness is a concern for many parents. I would get asked that a lot. My own son is also shy and we were worried about he would be on the day (even though one of the schools was my own!).
Everyone is different and small things can set them off, so it is important that you set the scene so they know what to expect.
I just commented on the post about 4+ and separation anxiety, so look there for some top tips that I posted.
How is he at nursery? If he is more sociable there, I would say that the staff doing the assessment are very experienced at dealing with this age group and we can usually get most children to relax and get through the session - so it might not be too serious a problem.
In answer to your other questions - yes, it is possible to get in, they just need to be able to speak enough to get everything down. Some schools are a bit stricter on upset/super quiet children than others. I always say that it is perfectly reasonable for a 3yr old to be wary of being handed over to a group of strangers in a strange school! It's how they regulate their own feelings in the session to get through it that the staff are looking at.
And finally, yes I am sure he would flourish there. Or, where ever he goes. My son is much less shy than he used to be (he had a speaking part in the summer play and nativity!), it just takes some children a little longer to come out of their shells.