AC cord for cdp

I just ordered a Dacmagic from Cambridge Audio. The manual states not to upgrade the power cord, which is a 12 volt pin. If this is the case, would upgrading my ac cord on my cdp make any difference? Currently my cdp doesn't have a removable ac cord, but I was planning on upgrading it to one that did. However if won't make any difference I won't spend the money on a new cord. I'll hang up and listen to your responses now. Thanks.