The R"Y me'Orleans (quoted in the Background to the Daf) explains that the reason why Shechitah is not an Avodah is because it is not logical to say that that which is required to permit even non-Korbanos to be eaten is part of the Avodah. However, it does not seem to be obvious that the regular requirement of Shechitah and that of Kodshim are one and the same. For example, would a Ben Paku'a offered as a Korban be valid without Shechitah?
Moshe Ben-Zev, Yerushalayim
A Ben Peku'ah is not accepted as a Korban because it is a Yotzei Dofen, which is Pasul for Hakravah. Even though Rebbi Shmon considers a Yotzei Dofen to be a full-fledged birth, he admits that it is not valid for Hakravah (Nidah 40a). Every animal which was removed from the mother after the mother's death is considered Yotzei Dofen (Chulin 38b).
There is, however, a single opinion (Tana Kama in Bechoros 57b) who allows a Korban that is Yotzei Dofen, in which case your question returns.
The answer is that a Ben Peku'ah is certainly Pasul for a Korban because Shechitah cannot be performed on it a second time (after the Shechitah of its mother while it was in the womb). A Ben Peku'ah of Chulin is permitted because it is already slaughtered. A Ben Peku'ah of Kodshim is Pasul because it was "slaughtered" before it was fit to be brought as a Korban (and since it is already "dead and slaughtered" it cannot be re-slaughtered).
Best wishes,
Mordecai Kornfeld