You can get regular cars up to the top of Mauna Kea (I saw some up the when I went to the summit) but it can be tricky on the steep gravel and rental car T&Cs have clauses prohibiting taking them up there. If you do go up they won’t be covered by any insurance or recovery so an incident or needing recovery because the car is stuck gets very expensive. On the way down the gravel section be careful not to overheat the brakes.
It is perfectly possible to do the regular ride up Mauna Kea without a guide. You just cycle up the saddle road and take the turn up to the ranger station and summit. Keep going until the top.