What medication is best for mild high blood pressure w/o risk to asthmatic & w/o even the 1% possibility of hair loss?

Your doc can choose: We usually avoid a class of med called beta-blocker in treating BP in asthmatics, but beta-1 selective bb has minimal effect on asthma. Aldactone (spironolactone) can reduce hair growth, but only used in heartfailure or severe bp. BP meds generally don't cause hair loss unless BP is drastically n rapidly reduced (reducing blood to scalp) which may affect hairgrowth for first few months. Minoxidil causes hairgrowth.

Hair loss: Rather than look for the drug which will absolutely not cause hair loss, perhaps you should pick a drug with a smaller chance of this happening, with the understanding that unexpected side effects occur with most medications. Spironolactone is a realtively weak diuretic, but is less likely to cause hair loss than beta blockers or calcium blockers.