I want to make something clear: the birth control pill only increases the chance of heart attack, stroke and blood clots. I have never heard of anyone having any of the three because of taking the pill unless they had a history of heart disease, high blood pressure, blood clots... So, if you have never experienced any of these, chances are slim that they would happen to you. Also, smoking and age dramatically increase the chances of these three illness, so smokers and women aged 35 or older who take the pill are much more likely to suffer from the three.
I think you would be safest with the use of the condom and an additional form of birth control such as hormonal birth control pills or spermicide.
But that's just my opinion.