USE THE MOSQUITO NET. Even if you are in a hotel room that is air conditioned. ( but ESPECIALLY if you are in an open air environment ) It's the BEST way to protect yourself from mosquito bourne illness, period. Carry a small kit with a few cup hook screws so you can effectively hang the net. Trust me, you can fill the small hole from the screws with toothpaste and no one will know.
Might I suggest those 3M Command Adhesive Hooks you can find in the grocery store instead? They stick quite well, hold quite a bit of weight, and are fully removable with no damage to surfaces.
I do however like the idea of filling holes with toothpaste! Besides, some hotels deserve a few holes in the walls. They'd probably improve the decor in some of those rooms.