No, breaking (by break I assume you mean a pre-image attack) SHA256 or SHA512 will not effect your private keys at all. SHA256 is not used in anything related to key derivation. SHA512 is used in key derivation, but you don't actually know the SHA512 hash unless you have a private key from the wallet, and even then, you only know half of the hash, not the full hash, so you can't find the preimage which would be the parent private key. These hash functions really are not involved in hardware wallets at all.