Let's start with Colossians 2:11-13. Here is the text -
11 and in Him you were also circumcised with a circumcision performed without hands, in the removal of the body of the flesh by the circumcision of Christ, 12 having been buried with Him in baptism, in which you were also raised with Him through faith in the working of God, who raised Him from the dead. 13 And when you were dead in your wrongdoings and the uncircumcision of your flesh, He made you alive together with Him, having forgiven us all our wrongdoings,
Please note the following:
1. There is no mention of any covenant, either old or new, and, therefore it cannot be understood that Paul is making reference to either covenant.
2. There is no equivalency stated here. If there was Paul would have probably written something like this: "and in Him you were also circumcised . . . . . . therefore, corresponding to that circumcision you have been circumcised spiritually with Him in baptism" but he did not, obviously.
3. Paul states these as being sequential events. First you were circumcised spiritually (performed without hands) then you were buried with him in baptism (an operation performed with hands).