Frame it by mechanism: non-obstructive retention means the detrusor will not contract, so you want a cholinergic 'push', not an alpha-blocker that merely opens the outlet.
Bethanechol is a synthetic choline ester selective for muscarinic receptors of the bladder and gut, and unlike acetylcholine it resists cholinesterase, giving a sustained detrusor contraction. That makes it the classic choice for postoperative and postpartum bladder atony.
Eliminate the rest: methacholine is a provocation agent that can trigger bronchospasm, dangerous in a COPD patient; terazosin and tamsulosin are alpha-1 antagonists suited to outlet obstruction in BPH, not to a flaccid bladder. So bethanechol is the answer.