You simply go to 2-3 intermediaries and maybe also to 2-3 banks (or even insurance companies) and in the end you compare the offers and take the one you like best. You are overthinking it too much in advance.
This is a recommended procedure for requesting terms for real estate financing.
If there is interest in taking out a term life insurance policy, the procedure is usually similar: You commission an independent insurance broker (some are also specialized in mediating disability insurance and term life insurance, especially regarding complicated cases) to make an anonymous preliminary inquiry to different insurers. This procedure is important because each potentially rejected application (for health reasons, for example) is stored in the aforementioned HIS database and thus makes any further application more difficult or impossible.
If one knows that taking out a term life insurance policy will be very difficult to impossible due to one’s medical history, one can also inquire about other credit insurance options. There are a few, but these are usually more expensive and do not cover as broad a spectrum of contingencies as a term life insurance; often, for example, only the death of the borrower is insured, but not severe illnesses etc.