Create BIP-85 wallets within Coldcard and use one of them for your KYC bitcoin (don't mix with any KYC-free funds).

With BIP-85, you can create as many wallets as you want (up to 10k wallets).

Then connect your cold card with Sparrow wallet (using SD card (air gapping)) and start coinjoing your KYC funds on Sparrow.

You will have to create a third wallet to receive the coinjoined (mixed) funds back as they will be clean.