Ometepe, being a volcano rising out of Lake Nicaragua, is of course, covered with volcanic rocks. I got my in a pair of running shoes, but was there in May, which is closer to the beginning of the rainy season, whereas August will be smack in the middle. I still think you can get by in sneakers. Take the trip to the top of the volcano, and explore around as well. I was most impressed with getting off the road and into the woods. The rocks were everywhere, and it was like walking on jetties, with huge trees just growing up in the middle of these volcanic rocks. Watch your ankles.
When it's not cold, I'm not abig fan of raingear. The showers are usually brief, so i wear something quick drying, and let the rain cool me off.
The ferry ride from Rivas was pretty impressive. The lake kicks up pretty fast, and the island surf can be very rough, so take care.