[Will the mixed coins be private if sent back to the originating cold storage wallet (which held or still holds some Coinbase coins) l as long as I practice proper coin control (e.g., never combining mixed coin UTXOs with Coinbase UTXOs)?]

I have a stack of Coinbase KYC Bitcoin in cold storage, using a hardware wallet.

I would like to Whirlpool Coinjoin mix my KYC coins for better forward privacy. I would like to use the minimum number of wallets, steps and keys to achieve privacy.

In Sparrow wallet you have to open a "hot" software wallet to Whirlpool them.

If I send my KYC coins to the new hot wallet, mix them, and send them back to the original cold storage (using new and unique receiving addresses, of course) wallet where the KYC coins were stored before...

Will the mixed coins be private if sent back to the originating cold storage wallet (which held or still holds some Coinbase coins) l as long as I practice proper coin control (e.g., never combining mixed coin UTXOs with Coinbase UTXOs)?

Or, is a wallet "contaminated" with my identity once it received a lot of KYC coins and it would be most private to send the mixed coins to a new wallet?

What is the simplest way for my to get my Coinbase funds out of Cold Storage, mix them, and send them back into cold storage without losing my privacy on the new coins?

[What is the easiest way to have two separate, relatively private (unconnected on the blockchain) stacks of BTC with the minimum number of devices, keys and passwords / phrases to manage?]

I am new to Bitcoin and want to set up 2 separate wallets or "stacks" of Bitcoin to HODL in cold storage. What is the easiest way to have two separate, relatively private (unconnected on the blockchain) stacks of BTC with the minimum number of devices, keys and passwords / phrases to manage?

I was considering putting Coinbase funds on a hardware wallet and then setting up a "passphrase" for an additional wallet (on the same device) to store my P2P coins. Will that keep them separate on the blockchain or can 3rd party observers see that one public key controls both those 2 different wallets and see the balances for each?

Or do I need two hardware wallets for better privacy?

thank you in advance.