Are there any tours of Cape York that operate in April?
There are many tour operators working out of Cairns, so look up Cairns tourism in your browser. However, many of them will be touristy (Cairns is a major tourism centre). Nothing wrong that; but if you want a real outback experience, search “Cooktown” (it’s a bit of an adventure just getting to Cooktown). Last time I was there, the local taxi company did tours for small groups into Cape York; but that was a few years ago. April is an Ideal time to go (at the end of the wet season). Cape York gets 75% of its rainfall between November and March.