You can tell the device you want a new random secret (so now your existing credentials don't work), but you can't get the secret out (obviously bad guys would use that, so it would be a terrible idea) neither can you set the current one to an explicit value.

You definitely can initialize Yubikey OATH-TOTP with a known value in order to have multiple devices with identical secrets. I have done that, also see https://support.yubico.com/hc/en-us/articles/360016614880-Ca...

So you can set the current one at the start of your use and keep the secret hidden somewhere forever. Sounds like the solution to me.

Evidently the way I wrote this previously wasn't clear enough, so I have attempted to improve this text.

No, you can have a random new value (effectively like you bought a different one), but you won't learn what that is, so it doesn't help you and there's no way to "keep the secret hidden somewhere" except in the sense that it's hidden inside the device where it belongs.