There's no restriction to having laminar flow when using a pitot tube. If there are flow straighteners (highly recommended) then the rotational flow should be minimized. The only thing left to do is to make sure that the measurement is taken in a section with fully developed flow. That way you don't have to do a traverse and integrate to get an semi accurate measurement since a fully developed turbulent velocity profile is pretty flat.
The best way to do it is to separate the static pressure measurement from the dynamic pressure measurement. Take the dynamic measurement via the pitot tube. Do not have the static ports on the tube itself. Take the static readings via static ports on the wall of the tunnel. This does assume that you've done a decent job at flow straightening and are fully developed.