Certified GKH Gardening Expert
Normally, although it is very dilute already, you will dilute the peroxide even more before you use it. The oxidization is too much for some plants, so it is best to test small amounts first.
I would say that it can be safe to replace 1/4 of the water in the mix with peroxide. I just wouldn't recommend doing that full strength. This is especially true since using neem oil already carries a risk of damage to some plants. This is exacerbated by intense light and heat. Adding too much of an oxidizer may intensify this as well.
If you do intend to experiment with this, make sure to dilute it out and replace only small amounts of water at a time.
There are many other ways to battle fungus, as well. This article will give you more ways: https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm