We had our 4 year old tested with WPPSI, after just having turned 4 years. I managed to find a psychologist to test dd who is basically an extremely gentle kind older woman, just the sort of person that a little girl would warm up to, or any small child. I think the tester will be a question you have to tackle as well. But getting with the school to find out what they would accept for either grade skipping or for a gifted program is a very good idea. Putting your son in school and then waiting for them to test will likely be very difficult for him.
Of course it seems totally odd to be asking for testing for a 4 year old, but once you have results to show people it makes the conversation WAY easier; the big circular conversation about whether or not the child is even gifted is (usually) concluded, and you can move on to what to do for them.

Best of luck!