FWIW, my DS hated PS at 2.6mths (well, cryed when I left etc.), and was "ready" for it at 3 (ran in, with never a backward glance). At 3 and a half, he loves it. If you feel your LO would be better off waiting another 6 or 12 mths before attending (or even not at all), so be it - you're his mum, not a pediatrician who has read it out of text books.
Mother and toddler groups are a nice way to ease kids into social settings - with someone to back them up on hand all the time. Similarly, you could organise visits from and to other small children's homes, where your LO could learn to play with others in a calmer and quieter environment, and you would be able to keep a discrete eye on things.
i have a non shy and non sensititive 3.5yo who has no official speech delay but whose speech is very unclear. he soemtimes gets frustrated at nursery as often the other children cant understand him. it was probably easier at 2.5 as only a minority of children are clear fluent speakers at this age
i guess it depends how his shy persoanlity will cope in the group situation
and whether he will end up being left out by the others because they cant understand him
or maybe his speeech will improve dramatically by mixing more with other children
but i guess if nursery was the answer to all speech problems then there woulndt be any SALTs working with pre schoolers, woudl there?
He's 2.8 years old,they don't all talk and have bags of confidence at that age. Be patient go with your instincts. If you don't think he's ready don't do it,he'll get more frustrated trying to make strangers understand what he wants etc. My son was referred to a speech therapist at 3, developed a stutter at 3/4 and went to school speaking fine at 4 and half. go with the advice already given thats the best you can do for him.