What is the age of your father? is his EF which you mentioned currently at 40% is deteriorating or is stable. his discomfort is constant or it increases on exertion. how far can he walk without being breathless and what is his current medication. these questions need to be answered before we jump to advise or refuse an angiogram in this case.
if his EF is stable, his symptoms are only on rapid strenuous exercise, then perhaps adjustment of medication is all he will require but if his EF is decreasing or he is having symptoms on minimal exertion , then perhaps after adjusting medicines, he may have get an angiogram done.
all these will be assessed by your cardiologist before he takes a decision.
needless to say a good control of diabetes
is a must for your dad.
please discuss all these aspects with your cardiologist and revert back with any further query.