MixedUnit["RightAscensionHMS"] and MixedUnit["ArcDMS"] worked successfully. Here is the content.
ap = AstroPosition[
Entity["PlanetaryMoon", "Moon"], {"Equatorial",
DateObject[{2010, 1, 1, 0, 0, 0.}, "Instant", "Gregorian", 0.,
"TT"]}]
AstroPosition[{104.45357536810378`, 23.50152305129125, \
0.002402213329988384}, {"TETE",
"Date" -> DateObject[{2010, 1, 1, 0, 0, 3.92901711165905*^-8},
"Instant", "Gregorian", 0., "TT"]}, "RADec"]
UnitConvert[Quantity[ap["RightAscension"], "AngularDegrees"],
MixedUnit["RightAscensionHMS"]]
Quantity[MixedMagnitude[{6, 57, 48.8580883449}],
MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension",
"SecondsOfRightAscension"}]]
UnitConvert[Quantity[ap["Declination"], "AngularDegrees"],
MixedUnit["ArcDMS"]]
Quantity[MixedMagnitude[{23, 30, 5.4829846485}],
MixedUnit[{"AngularDegrees", "Arcminutes", "Arcseconds"}]]