The Remah in O.C. 178:1 gives a general definition of Chukat HaGoyim. There are three kinds of practices that are included in this prohibition:
1) Things that are done for purposes of promiscuity.
2) Things that have no rationale- i.e. superstitions.
3) Practices that have traces of idolatry.
It would be difficult to conclude that the Remah would hold that wearing black for purposes of mourning would be Chukat HaGoim.
(That being the case, the Vilna Gaon has a broader definition of Chukat HaGoyim...)
Indeed, the Torah itself testifies that mourners wear black. The מדרש שכל טוב explains that Tamar's garments of mourning were black.
See also the Remah in E.H. 17:5 (cited in a previous answer) where he refers to the practice of widows wearing black.
(Of couse, the above refers to mourning in general, as opposed to the funeral itself. Perhaps, there may be specific styles of mourning costume which may be problematic, at least according to the Vilna Gaon. There may also be a concern for introducing new customs into established Jewish ceremonies, even where there's no concern for Chukat HaGoyim itself.)