Although blowing the shofar is prescribed by Torah law, under certain circumstances Rabbinical decrees can override it and actually prohibit blowing the shofar entirely. The Sages determined that one must forego a positive Torah commandment if the alternative would be to transgress any Rabbinical prohibition. Therefore if a shofar was buried under a pile of rocks or another type of object that is forbidden to move on Yom Tov, or if was resting on a tree branch or beyond the 2,000 cubits we are permitted to walk, or on the far side of a river, we simply cannot fulfill the mitzvah.
Although a Jew is not permitted to ask a non-Jew to do a Torah prohibition for him on Yom Tov, it is permitted to ask him to do a Rabbinical prohibition when a mitzvah is involved. Thus the Mishnah Berurah (586, 21 s.v. 86), citing the Chayei Adam (140, 19), writes that if a shofar must be brought across a river by boat, it would be permitted to have a non-Jew transport it, if no other option is available.
The Mishnah Berurah adds that even if you had a type of shofar other than a a ram’s horn shofar, it would be permitted to have a non-Jew bring a ram’s horn shofar, which is considered the preferred way to fulfill the mitzvah