I was skipped at three different districts. But we moved a lot and I started the process all over again with my age peers.
The first was in Montessori and the first skip was into 2d after K, and then into grades 4-7 from 2d in the middle of the year. There was no testing the waters.
In another district, they put me into reading for 6th and then into Math for 5th before I skipped.
The last time was from 7th to 10th. I was tested when I first arrived in the district and placed with my academic peers. I did PE first period at Jr High then walked over to the HS for class starting 2d period. I also played on the Jr High football team and freshman soccer team at the HS.
There were other districts that did not skip.
My DW was skipped from K into 2d at the end of K. No water testing either.
The testing and then placement with his academic peers might be the route to take.
