Some X apps and window managers accept a "-display" command line option. Some use "--display". All appear to honor the DISPLAY environmental variable.
This bit me some time ago with the Debian menu system, which facilitates changing window managers on-the-fly. Switching to e went horribly wrong because it didn't know what DISPLAY to use. There may be a better way to do this, but no one has complained in the couple of years that I've carried the patch.
--- enlightenment-0.16.6-upstream/src/session.c 2003-11-05 12:58:51.000000000 -0500 +++ enlightenment-0.16.6-debian/src/session.c 2003-11-06 05:07:03.000000000 -0500 @@ -1196,7 +1196,7 @@ #endif XCloseDisplay(disp); disp = NULL; - Esnprintf(s, sizeof(s), "exec %s -display %s", atword(params, 2), dstr); + Esnprintf(s, sizeof(s), "DISPLAY=%s exec %s", dstr, atword(params, 2)); execl(DEFAULT_SH_PATH, DEFAULT_SH_PATH, "-c", s, NULL); } else if (!strcmp(s, "restart"))