It is IMPERATIVE that you do any type of diet/exercise modification under the guidance of your doctor! You cannot rely upon the opinion of people on this board when it comes to something so critical.
As to whether Atkins can be done by someone with a heart condition - yes, indeed! My uncle (who is only 57), drove himself to the emergency room with chest pains on his way to work one morning. They admitted him, and found that they had to do a quintuple by-pass!

Once out of the hospital, his doctor promptly put him on the Atkins plan.
Having said this, I must stress once again - ANY DIET/EXERCISE MODIFICATION SHOULD BE DONE UNDER THE SUPERVISION OF YOUR DOCTOR!
Best of luck to you!