I think they do have different derivation paths which is why it won't conflict with any issue.
The derivation path is wallet dependent, but it is irrelevant. An identical key at an identical path can be used in both a single-sig and a multi-sig wallet simultaneously without issue.
The keys from a single key wallet is of different type of compared with the keys of multisig wallet. If you take a close look at it, the private key from a single key wallet starts from xpub, ypub or zpub, but it start with Xpub or Zpub in multisig wallet.
This is true only for extended keys, not individual keys. Individual keys are indistinguishable, and a private key at any derivation path can be used to generate any type of wallet or address. (Also, xpubs are extended public keys, not private keys.)
Wanted to use one of the keys I've already stamped in steel washers for the single SIG. I didn't think there would be any issues, just wanted to make sure
Have you stamped an individual key, or a seed phrase?
If you've stamped a seed phrase, the only issue I could see was if you then extracted an individual private key from your multi-sig wallet to use as a single-sig private key, then you could very well run in to major issues in the future trying to recover that from your back ups. If you are simply taking the seed phrase and using it to generate a brand new single-sig wallet as normal, then there will be no issues.