Haven't climbed Mauna Kea but did Mauna Loa 2.9 x. I climbed from the "strip road" on the E., from Volcanoes Park, or from the NOAA Observatory (which I visited on TDY on the way to being posted at the one in Barrow AK!)(did visit Pt. Barrow, N'most point of US).
However, in a visitors' register on the summit or at Puu Ulaula hut (cabin) on the way up, or Mauna Loa cabin (el. 13 250) on the crater rim, I found an entry from people that climbed from Capt. Cook or Honaunau on the W. or Kona side. This would be a real adventure; there's no trail.
I considered hiking down the W. side but was told it was unwise alone due to lava tubes (if I fell in one) or pakalolo plantations in the "forest reserves" far down the Kona side. But it's a trip I've always wanted to do.
I also met someone who hiked the SW Rift Zone, no trail either. Hiking round and across the huge Mokuaweoweo Caldera was enough for me.