When I visited Kauai in 95 I asked about climbing Waialeale/Kawaikini, but all I got was "there is no trail". Extensive enquiries a few years later got one reply that "people trying to climb it are cited", something to do w/environmental issues. On a topo map of the island, the NE ridge offers a possible route from the Power Line Trail, which crosses it; but I couldn't tell from the map how difficult this ridge is. It could be a broad easy one; covered with impenetrable growth; or a jagged sheer eroded crumbling nightmare. Visitng Koke'e State Park on a beautiful clear day, the summits were visible across a plateau, not much higher; but it was the notorious Alika'i Swamp. The trail across part of it had boardwalks but they were incomplete and beyond that it was very muddy (it goes to a lookout, but I turned back). One chap did report reaching the summits across it.
W'le is supposed to have the world's biggest rainfall--another obstacle--while its neighbour K'ni is a bit higher. One newspaper article showed a rain gauge atop W'le but not how to get there; I suspect they took a helo up on a fine day. I took a helo tour later & the whole area was engulfed in rain clouds. There is supposed to be a heiau (temple site) on top so the natives must have known a way up. Good luck; be sure to report on your attempt.