We don’t have a doctrine declaring CP immoral per se - that would be diametrically opposed to the doctrine that it is not intrinsically evil.
I agree with this, but if this is true then it is an error to act as if it wasn’t, and saying this comes with some significant problems. What does it mean to say that capital punishment is now inadmissible? If it is not intrinsically evil then it must be admissible in certain cases (by the meaning of the terms), but that would mean it’s not actually inadmissible.
It is also asserted that its use is contrary to man’s dignity, but again, if it is not intrinsically evil then either acting contrary to man’s dignity is justifiable, or it’s not in fact an offense against that dignity.
We have a statement that in our times killing criminals is immoral in light of circumstances. You may be right that resting on circumstances renders the statement prudential, though clearly if the judgements about circumstances are correct, then the act would be “immoral”.
If its use is valid depending on circumstances then that clearly involves a prudential judgment about which circumstances render it beneficial or harmful, which reinforces the problems I cited above.
As to whether an erroneous judgment about something is sinful I would say it is not. It would be a mistake, not a sin. If I believe the consequences would be harmful and support it anyway, that would be a sin, but if I believe the consequences to be beneficial and support it, whether mistakenly or not, that can be at worst a grievous mistake. Mistake are not sins
It seems you sensed this when you put quote marks around “immoral”.
If you hold that capital punishment is not intrinsically evil it means it cannot be considered inadmissible, cannot be contrary to man’s dignity, and support for its use cannot be broadly condemned as anything other than an error of judgment…which is your opinion on the matter.
It has always been my position that the decision about whether to use the death penalty is prudential judgment about which disagreement is legitimate, and while there may be valid practical objections to its use there are no valid moral objections.
If you recognize that it is not intrinsically evil then accept the implications of that position.