You will unfortunately have to install addons for this as Blizzard does not give a built-in option for enabling or disabling specific sounds. Here is a guide on how to install addons: https://www.wowhead.com/guide/addons-how-to-install-and-maintain-1998 easiest way is to install the CurseForge application: https://download.curseforge.com/ There are three options I know off for this:
1. Muting only the loud screeching sounds (made by me)
Install the WeakAura addon: https://www.curseforge.com/wow/addons/weakauras-2
Go to my WeakAura here: https://wago.io/SbSROX7aR and click the button "Copy import string". Open WeakAura addon in-game by typing /wa in the chat. Click the button "import string". Paste the content from my weak aura and click Ok.
2. Muting all screech and landing sounds
Install the WeakAura addon: https://www.curseforge.com/wow/addons/weakauras-2 Go to the WeakAura here: https://wago.io/SDhHuZh3f and click the button "Copy import string". Open WeakAura addon in-game by typing /wa in the chat. Click the button "import string". Paste the content from the weak aura and click Ok.
3. Muting all mount sounds
Download Leatrix Plus addon: https://www.curseforge.com/wow/addons/leatrix-plus. Click the Leatrix Plus button in-game which is around the minimap. Go to "System" and click on "Mute mount sounds" and then the configuration settings button and click the checkbox for "Dragonriding". If you have already modified Dragonriding sounds previously, you will have to quit the game and log in again for changes to apply.