Seems at though he can appoint whomever he pleases to fill the vacancy with, regardless of party.
http://legis.state.sd.us/statutes/DisplayStatute.aspx?Statute=12-11-4&Type=Statute
South Dakota Constitution
12-11-4. Temporary appointment by Governor to fill vacancy in United States Senate. Pursuant to the Seventeenth Amendment to the Constitution of the United States of America, the Governor may fill by temporary appointment, until a special election is held pursuant to this chapter, vacancies in the office of senator in the Senate of the United States.
Source: SL 1979, ch 99, § 1.
Oops. Double post.