The preventative heart health program i linked above at Stanford does an echocardiogram calcium score rather than a CT scan for the first phase. Saves you from radiation unless they see something that warrants it.

It is no issue at all to ask for and receive an echocardiogram referral since it has no risk, just ask for a referral.

The unwillingness to do anything involving radiation unless warranted seems reasonable. Just do the echocardiogram and go from there.