I learned that something that is on a tree bein hashemashos Friday evening is muktzah the whole Shabbos.
Let us assume that there is a shofar on a tree bein hashemashos of R”H. A Jew may not climb the tree during R”H to retrieve his shofar. However, I believe that he may request of an akum to climb the tree.
So how will we blow this shofar if it is muktzah?
The shofar doesn’t become muktzah,never the less one is not allowed “miderabonon” to climb up the tree to retrieve the shofar. Asking a non Jew is permitted because it is a “shvus deshvus bemokom mitzvah”.
O:CH 586:21 & Mishnah Berurah 86