Mini-seed of single utxo
With existing standards and wallets, no, that is not possible.

Existing standards such as BIP 39 do not directly use the value encoded by the words to produce a BIP 32 HD seed for use in a wallet. Instead they hash the words.

Furthermore, wallets that import that mnemonic do not just use the BIP 32 HD seed from it directly. Instead they use it with derivation paths and derive child keys from it.

If you produced a mnemonic from an individual private key, importing it into any existing wallet would not result in your private key being imported. You would end up with things derived from that private key, but that is not useful to you.



Instead of a mnemonic sentence, what you really want are the Wallet Import Format (WIF) private keys that most wallets can export. WIF is a standard way to encode individual private keys so just use that instead.