Your Dad will be fine. The good thing about an Angiogram is that he will be awake, able
to tell the cardiologist if he feels anything strange. If any blockages are found then they
can be treated there and then without the need for further appointments.
An angiogram can be performed with a cath (intervention with a probe through the leg vessel to the heart), or ct scan (best is a 128 slice) that views the blood flow (dye has been injected) through the coronary arteries.
There isn't a high risk with a cath, and it is not painful, but have an understanding with the doctor whether or not your father wants a stent implant if there is some blockage, and whether the stent(s) are drug coated or not (obtain an opinon what the doctor prefers). It seems drug coated stents have a higher risk of of forming a clot within a year.
You don't state your father's condition, or if there are any meaningful and sigfnificant symptoms.