An alternative to the Inca trail would be the Lares Trek. Almost sure this is happening still in April. I highly recommend it. I did it with GAP adventures and not sure if it was luck but the only other tourists I saw for the 4 days was us. Absolutely amazing experience. A wonderful way to see the countryside and interact with the locals who live on those very mountains. The Lares Trek - look into it!
Some Info about the Lares TrekYou can do some research on Google to see what would be the best tour company to choose. I had a great experience with GAP adventures but I think that the prices have gone up since I've been maybe there are others that are cheaper. Definitely worth doing.