I know the shofar is not to be blown on rosh hashana except when performing it for a mitzva, but is a shofer permitted to be blown when it is not shabbos or a chag for recreational (not mitzva or mitzva preparation) purposes?
Assuming the Shofar was not previously blown for a mitzvah:
Yes, as explicitly written in Psalms 150:3, where the shofar is listed among other musical instruments:
הַלְלוּהוּ, בְּתֵקַע שׁוֹפָר; הַלְלוּהוּ, בְּנֵבֶל וְכִנּוֹר.
(See also Ps 81:4, 98:6)
In addition, the Gemara (Rosh haShana 33b) includes a discussion about whether one fulfills his mitzvah obligation if he blew "to make musical sounds" on Rosh haShana, implying that one is allowed to use a shofar to make music.
Finally, there are many cases in Tanach where a shofar was blown for non-mitzvah purposes, (mostly involving wars and coronations; Shoftim 3:27, 2 Samuel 2:28, 1 Kings 1:34, 2 Kings 9:13, Amos 3:6, among others), and the Gemara (Shabbat 35b) mentions that a Shofar is blown on Friday to tell people to prepare for Shabbat.