It seems that the Gemaras that say that the learning of the parshiyos of the korbanos is considered as if one has brought those korbanos is contingent on the person’s intentions. If one reads the parshah without thinking that his learning of the parshah should be considered as if he has brought a korban, it will not be considered as though he did. The tefillah that was instituted to be recited after one reads the parshah was established to ensure that one’s intentions are to render the reading as if he has brought the korban.
I believe that if one was not required to bring a certain korban and still recited the parshah of that korban, Hashem will not consider that recitation to have been to his detriment. Thus, in a scenario whereby bringing a korban could be problematic, we do not recite the tefillah; we leave it up to Hashem to decide whether this recitation should be considered as if the individual had brought a korban. Consequently, both on Shabbos and according to the Tur regarding a korban chatas, the tefillah should be omitted.