Of course, I don't know anything beyond what you've told us about the specific examiner, but, in general, early childhood evaluators are very accustomed to the behavior and varying levels of attention and compliance of young children. I don't do littles much anymore, but when I did, I absolutely tested children while they were under tables, spinning, dancing, in 15 minute increments, rewarding them with stickers every few items completed (lots of stickers!), taking turns (you draw a picture, and then I'll draw a picture), etc. I've sat under the table with them, given them fidget toys to play with while testing...pretty much done everything except stand on my head in the quest for optimal performance (can't do a headstand). I think I may have tested a stuffie once.
Naturally, you should do what you think is best for your son, but I would put a caution in about sitting in for any portion of testing. Children, especially very bright children, are very savvy about cueing off their parents' (and the examiner's) reactions to their responses. If you are in the room, make sure you are somewhere that he cannot see or hear you. Many children give up more easily if adult feedback conveys to them that they are answering incorrectly. He knows you very well, so he will be able to read your "tells" much more easily than another person's. You might be better off giving the examiner a few examples of the kind of careless responding that may obscure his true abilities, along with some of his specific skills, in a private conversation out of earshot of your son.
I would agree that the cognitive test is the WPPSI-IV, a very appropriate instrument for this age and ability. If you need re-testing, the re-test interval is a minimum of two years from the last administration, if giving the exact same test. In two years, he will be seven, which would move him up to the WISC-V. In fact, you could have him re-tested with the WISC-V at age 6.0, in exactly a year. If you really need re-testing sooner than that, the SBV is also a solid instrument, with a higher ceiling than the WPPSI-IV, actually. The WJIV cognitive would also work, but it has some normative limitations for early childhood.
I wouldn't get too far ahead of yourself, worrying about having to have him re-tested. Keep in mind that IQ scores are quite unstable at this age, so even if he doesn't test at a number consistent with your everyday experience of him, it doesn't necessarily mean it was a bad test. Little children are just a bit unpredictable in their response to and presentation on testing. It's more important to focus on the information, guidance, and supports you get out of testing, than on the precise numbers.
Oh, and the brief test that he just had is likely a kindergarten screener, which is designed mainly to pick up children with delays in one of the Big 5 areas of development. They tend to have low ceilings, as the objective is child find for children at risk for disabilities and developmental delays, not actual IQ. Many of them are reported simply as above or below a cut score.
