The simple approach is to go 20mmHg higher than your initial BP from in the house (or before wheels were rolling) and listen from there down.
If that fails, go to a palp pressure and then go 20-30mmHg above that, and listen from there down.
If that fails, you at least have a by-palp pressure.
If that fails, go to pulse quality. While a positive radial pulse likely means a BP >80mmHg, it doesn't necessarily mean that; I've had septic shock patients with radials and BP's <80mmHg.
Correlate their palpable pulses with their mental status: answering questions appropriately and without hesitation? Joking with you? Those are higher level mental functions which require adequate perfusion. Their cerebral perfusion pressure is most likely greater than 70mmHg!
If their CPP is >70mmHg, this means their mean arterial pressure (MAP) is greater than 60mmHg!
If you don't have a systolic and diastolic pressure to use, think of MAP as: (CO x SVR) + CVP
CO = Cardiac Output
SVR = Systemic vascular resistance
CVP = Central venous pressure
So with radial pulses and good mentation we know that the patient is maintaining the appropriate level of Cardiac Output, Vessel Tone (SVR), and Blood return (CVP) in order to perfuse their brain!
Not being able to auscultate a blood pressure is going to happen on occasion, so give yourself credit for the appropriate level of examination. Document the secondary findings of an adequate blood pressure and you'll be fine.