BEP2 asset recovery tool after BNB Chain Fusion: how can 3rd party wallet users recover their tokens?

I understand that a recovery tool will be enabled on Dec 3 (ref: https://www.bnbchain.org/en/bnb-chain-fusion) for BEP2 tokens that have not been transferred to the new chain. According to the documentation (https://docs.bnbchain.org/bc-fusion/post-fusion/token-recovery/), BNB Chain Wallet and Trust Wallet will be supported.

But some BEP2 tokens are held in other non-custodial wallets that just come with a passphrase for the wallet recovery and a private key along with the address and path for each BEP2 asset in the wallet. So how can those people recover their BEP2 tokens? Can they use the BEP2's private key to recover it using the tool, and if so how?