Zevachim 14 - Walking with the Blood
According to Rabbi Shimon, if a kohen has the intent that the sacrifice is of a wrong, different type, and he has this intent while walking with the blood to the Altar, the wrong intent does not invalidate it. This is because walking is not a necessary step, and if the kohen is close enough to the Altar, walking may be altogether absent.
Said Resh Lakish, "Rabbi Shimon agrees about those offerings that are slaughtered in the Courtyard and then carried inside the Temple Hall (such as Yom Kippur offerings) that the wrong intention does invalidate them - since this walking cannot be circumvented.
Seeing that walking has somewhat lenient requirements, they asked Rav Chisda if it can be done by a non-kohen. Rav Chisda said that it can, quoting " and they slaughtered the Passover offering, and the kohanim threw the blood from their hands " - it must be that the non-kohanim who slaughtered also walked with the blood! However, Rav Sheshet disproved this, and as far as the quote, he explained that the non-kohanim just stood like pillars but did not move at all.
Art: David Roberts - Hall of Columns, Karnak, from Egypt