The peroxide that you buy is not going to eat great holes in your flesh, it's way too mild for that. It is an indiscriminate oxidiser, it donates an oxygen atom to anything oxidiseable and becomes water.
ie H2O2 > H2O + O- .
Point is, root tips are incredibly fragile, and no corrosive liquid, no matter how weak is going to do them any good.
H2O2 is very reactive, and almost anything will make it break down.

---------- Post added at 02:45 PM ---------- Previous post was at 02:42 PM ----------

An excellent fungicide is Mancozeb. At the first sign of potential trouble, a suspect plant gets bathed in the stuff.

Thanks everyone! I've been trying to learn more about orchids since 2015. This is the first time I have heard about not using hydrogen peroxide. I remember seeing Physan 20 at the local nursery and at Hausermanns.

I have not heard of Mancozeb before.

This might seem like a silly question, but is Physan 20 safe to go down a kitchen sink (I do some, but not all my watering there)? I also have cats, so I worry a little about using this. I suppose I could just put in spray bottle like I did with the hydrogen peroxide and use it over the potting tray only.

Is this toxic to people? I'm gonna to assume yes, but to what extent? Safe without gloves? Always use gloves? Shouldn't be in contact with food surfaces? Etc.?

Physan 20 is pretty safe for humans and other warm-blooded creatures once diluted, so I wouldn't worry about the cats. Probably not harmful on food surfaces, but just on general principles you'd probably want to clean it off. Remaining traces shouldn't be a problem. Small amounts of dilute Physan should also be no harm down the sink. (The concentrate would probably be an issue at the treatment plant, but not at the dilutions you would be using) About the only creature that I know it is quite toxic to is fish - don't use it in a fish pond or aquarium or anywhere near those! It attacks the mucus that protects the gills of fish and so can easily kill them. Spray bottle is a good way to dispense it anyway - you put it where you want it. So in general, the concentrate has some toxicity to humans, etc. but at the dilution that you use it, pretty benign if you don't have gills.

Even when I lived in St Louis, with humid summers, I didn't see much fungal trouble. I would suspect people would do better improving their growing conditions rather than running for fungicides unless they are growing in a really humid greenhouse.

I just don't believe somebody growing on a windowsill will get much fungus trouble if temperature, watering, air circulation and humidity are correct.

I agree about trying to keep your growing conditions tip top, but at the first sign or suspicion of fungus I hit it with mancozeb. Prompt treatment can save a plant, and if there is nothing wrong with it, Mancozeb won't harm it.