Your broker is correct to tell you that you should buy an individual policy as soon as possible, but he is right for the wrong reasons. Beginning in January of 2013, insurance companies are no longer allowed to deny coverage because of a preexisting condition, and certainly not because you have the potential of developing a condition that you do not yet have. The real reason you need to move away from COBRA is because COBRA is one of the most expenses methods of obtaining health coverage.
COBRA stands for the Consolidated Omnibus Reconciliation Act, and was implemented in the mid-1980's, The purpose of the law was to prevent employees from being unceremoniously dumped off their insurance coverage simply because of being laid off or terminated from a job. Under the law, you have to pay the full premiums, even the portion previously paid by your employer, as well as administrative fees associated with invoking COBRA. COBRA is only meant to prevent you from going without insurance while you are looking for replacement health coverage, but is not a form of insurance.
Invoking COBRA does not change your insurance coverage. Since you will be continuing the same insurance that you had, developing cancer would not create a preexisting condition at all, it would introduce a new medical condition that you did not previously have. It does not matter whether you have a family history of cancer; your condition is not preexisting until it has existed.
The primary reason to get new health insurance as soon as possible is because of the costs associated with COBRA. Depending on the portion previously paid by the employer, your rates could double or even triple when you invoke COBRA and that could create a financial strain on you and your loved ones. Even if you develop cancer while searching for a new health plan, you cannot be denied coverage under the ACA, but you may have to pay higher rates to account for the expected increase in cost of insuring you.