APPOINTMENT OF OFFICERS
The president is empowered, with the advice and consent of the senate, to appoint all embassadors, other public ministers and consuls, judges of the USSC, and all other officers of the US, whose appointments are not herein otherwise provided for... but congress may by law vest the appointment of such inferior officers, as they think proper, in the president alone, in the courts, or in the heads of departments.
A special prosecutor with the limited duties of investigating a narrow range of persons and subjects is an inferior officer. Therefore, under the appointment clause, congress is free to vest the power to appoint a special prosecutor in the judiciary.
Congress may not appoint members of a body with administrative or enforcement powers; such persons are officers of the united states and must be appointed by the president with senatorial confirmation unless congress has vested their appointment in the president alone, in federal courts, or in heads of departments.