they should have a database set up where people can register existing underlying conditions, so that they might qualify for the emergency financial measures past a point where people are being phased back into society.
the government would no doubt need to implement some kind of verification process, so this would no doubt mean the requirement of some kind of documentation from your doctor. this would be a necessary tool to protect against fraud, because people are assholes sometimes - i get it. they're taught to be that way; it's blowback. but, the process is required. fine.
the legitimate intent of the program would be to allow people to declare if they're at high risk, so that they can be quarantined for a longer period.
of course, such a list would have to be immediately destroyed after the pandemic is over, and with the inevitability of an electronic maintenance of said list, the likelihood of permanent destruction for some time is quite low. so, anybody volunteering themselves to enter data into a list of this sort would have to fully understand the likely near-term permanence of this information, despite any protocols to destroy it. that still may be a preferred option to people in high-risk categories, like heavy smokers or the obese, if they are fully cognizant of the threat of the disease to them, which may be uncommon.
i think the opportunity to opt-out for a while, with the proper documentation, should be provided, regardless.