Noachide Korban - this is going to keep me up nights!
By general rule, the Noachide korban cannot replicate the Jewish korban, but it would have to be carried out in a similar manner. There's matters of the mizbe'ach and it's construction.
Looking in the Torah I find in Bereishis 8:20 - Then Noach BUILT a mizbe'ach to G-d and took of every kosher animal and kosher bird and made burnt offerings on the mizbe'ach. I put an emphasis on "built" because this would compare to Bereishis 9:20-21 "Noach, the man of the Earth, debased himself and PLANTED a vineyard. He drank of the wine and became intoxicated..."
In both cases Torah refers to the preparation to the act. If you know anything about wine making, there is a considerable effort in cultivating grapes to produce wine. By the same token, the act of building the mizbe'ach is mentioned and one can infer that Noach's mizbe'ach took a significant effort to built. If it was merely a flat rock, the act of building a mizbe'ach would not be mentioned.
It would be a chillul Hashem to make a copy of either the copper or gold mizbe'ach, but the mizbe'ach would have to be something constructed in a manner similar to the way they were constructed and you have to consider things like the prohibition against striking the stones with iron. Good luck finding a shamir!
Assuming you can figure out how to build a mizbe'ach, your next challenge is that you would have to learn to be a shochet. An animal improperly slaughtered would be piggul.
At this point, one would think it would be wise start with small animals like kosher birds. There's another wrinkle there since birds were slaughtered using a technique called melikah where the kohen used his thumbnail to to puncture the back of the bird's neck and cut through to the front.
In the case of Noach, the Torah specifies a burnt offering. Burnt offering in the Jewish korban were not eaten, but burnt entirely on the outer mizbe'ach of the Beis Hamikdash.
I'm going to have to study this some more.