An angiogram is a procedure that images a contrast agent that passes through the vessels during rest and then with exertion to observe if there is any obstruction. There shouldn't be any risk with a CT scan, and if the procedure is with a cath the risk may be a problem at the entery site (groan) as a diabetic may have some difficuty with the healing process other risks are minimal i.e. rupture, uncontrolled bleeding, etc. Doctors are quickly available if there is a problem.
The word shunting means to bypass blood flow. I assume it is a coronary artery bypass, and the risk depends on general health and whether or not the conditions cited are under control, etc. Age shouldn't be much of a factor, but when 80 and above the doctor's carefully weigh the options (generally).