I've stayed in Corepen for 3 weeks in total. I can't recall seeing mosquitos!! I also did a one week long safari last January (moving from home stay to home stay between Mansuar, Arborek, Fam, Waigeo). Again very few mosquitos. I don't know ,maybe it's the season (always December or January for me).
To the OP:
Other than few clothes/swimsuit/toileteries/medicines you might need, there is not much.
- If you get hungry easily you'd better have some snacks with you as there are no shops around. Usually food is delicious and more than enough, but you never know.
- Also you'd better bring some soap/shampoo, although usually there are some left/forgoten there from previous travelers. There is no need to bring toilet paper.
- Some rain/water protection for yourself (puncho or something) and your bags (plastic cover?). You will have a half an hour long boat trip from Waisai to the homestay in a boat that has no protection from the rain whatsoever.
- Generally you won't need cash (they accept credit cards). Only exceptions are for tips and/or if you want to buy something from small local shops (assuming you move to other areas/villages - eg Arborek).
Enjoy your stay