If you're willing to use an NBT editor, this is most certainly possible, if you know where to look.

Prerequisites

• You have access to Minecraft: Bedrock Edition and Minecraft: Education Edition.
• You have an NBT editor that can edit MCBE and MCEE world files.

Step One: Get the world file.

There are two methods you may take to access the world file. You can either find the folder for yourself, or you may use the Export World button in MCEE.

• Method A: Direct folder access

  Windows 10 devices can use the following file path to find their files. Users on a different OS, sorry, I am unable to provide a file path for you yet. If you have one, please comment below.

  C:\Users\ExpertCoder14\AppData\Roaming\Minecraft Education Edition\games\com.mojang\minecraftWorlds
  

  Obviously replace ExpertCoder14 above with your actual Windows username.

  (ignore that this one has _UMCbackup, that's just from past experimentation.)

  Unfortunately the names of the folders do not provide any indication of which world is which. The only way to find out is to enter it and open the levelname.txt file there.

  Once you have found the folder that contains the world you wish to use, copy its entire world folder (not just levelname.txt) to somewhere you can easily access. I just put it on my Documents folder. Up to you.

• Method B: Export button

  You'll be able to save a .mcworld file to your computer by clicking the highlighted button in the image below.

  

  You should be able to open this file directly with UMCE. If your NBT editor does not support .mcworld editing, you'll need to convert it to an actual folder by changing the filename extension from .mcworld to .zip and extract the files into another folder.

Whew! You've successfully retrieved the world file. Now for step 2...

Step Two: Edit level NBT

Open your NBT editor. Go to the level.dat file of the world, and look for the Integer tag named eduOffer. Change it from 1 to 0. The following image shows where to find the correct NBT tag in UMCE:

Ensure that you save the file and then close it! Otherwise your changes won't take effect.

Importantly, if you chose method B from step 1, ensure you've converted the world back to .mcworld format before continuing. This will involve creating a compressed folder and then renaming the extension to .mcworld.

Step Three: Import the world

You'll need to follow a different step depending on which method you used in step 1.

• If you chose method A

  Move the edited world folder to the following Windows file path:

  C:\Users\ExpertCoder14\AppData\Local\Packages\Microsoft.MinecraftUWP_8wekyb3d8bbwe\LocalState\games\com.mojang\minecraftWorlds
  

• If you chose method B

  Use the import button in Bedrock Edition to select your edited .mcworld file.

It would be possible to create a custom resource pack that plays sound files that are just silence for the cave sounds.