Proceed to fix on final...
As an ATC, I'm pretty sure (and safe) about instructing/vectoring an aircraft to proceed to the IF for a straight-in APP, as far as I can also clear him to the IF published altitude. In case of this altitude being lower than my MVA, it would be always "pilot discretion" (if not in contact, totally unable).
In a non-radar TMA/CTR, I guess the same applies. The restriction comes from the minimum safe altitude at where the aircraft starts the procedure (IAF, IF or FAP/FAF). If I, as ATC, can clear the him to any /all of the published altitudes, go straight-in!
So, any shortcut is good as far as they can also be cleared to descent to the point where to join/follow the instrumental procedure.
PD: 3NM on final, is usually too low and to close to the RWY THR.