To the question
Hagoromo was a ~36cm nano satellite that was deployed by Hiten while Hiten was in a highly elliptical orbit around the earth, in 1990.
From there, Hagoromo was able to enter into an orbit around the moon. Also see this question and any answers that may be there.
How was this done exactly? Was it purely ballistic capture (which still requires a tiny amount of thrust I think?) or more of a propulsive maneuver to enter into a lunar orbit?
What kind of propulsion and attitude control (if any) did Hagoromo actually have?
the answer is:
From the NASA Space Science Data Coordinated Archive entry on Hagoromo,
A solid propellant (KM-L) retrorocket with a mass of 4 kg was mounted inside the spacecraft for orbit insertion.
Question: How could a tiny 36 cm nanosatellite with a 4 kg solid propellant rocket inside maintain attitude control throughout the burn in order execute an orbital insertion?
above left: from http://usi.kir.jp/CIA/ISAS/USI_cia_DS.html - models (presumably) of Hagoromo sitting on top of Hiten. right: from Gunter's Space Page Muses A (Hiten)