which apparently do not exist, since the naming convention does not technically allow for DB15
In the original naming scheme from the original manufacturer of the connectors, there was/is no such thing as a DB15.
The thing is manufacturers can come up with naming schemes all they like, they don't get to define the English language. The English language is defined by custom and practice among it's users, and yes this means that in some cases the English language becomes ambiguous or that you need to distinguish between different dialects.
Sometimes the "technically incorrect" usage becomes more common than the "technically correct" usage. Certainly growing up I remember it being the norm to use "DB" as a shorthand for regular D connectors regardless of the pin count. I don't remember encountering the "technically correct" nomenclature until Wikipedia started pushing it*.
Some people even use DB for the 15 way high density connector** I have personally always regarded this as wrong, but I may be in the minority here.
To check this wasn't just me, I went to the Farnell (a major electronics distributor in the UK). In the "D Sub Connectors" category I get 430 results for DB15 compared to only 42 results for DA15. Similarly I get 95 search results for HD15 and none at all for DE15.
can I go with my gut feeling and just pick out any 15-pin D-sub cable
In general you can't assume a cable is correct just because it uses the same connectors. The DA-15DA15 was used for many incompatible applications including the PC joystick port, the BBC micro's analogue input connector, the AUI Ethernet transceiver connection and the classic macintosh video output port.
Often hardware would have documentation of the pinouts in the user manual, so you could determine what cable was appropriate and buy or make one.
D sub cables were often, but not always, wired straight through connecting the same pin at each end of the cable. Some wires may be disconnected. Sometimes miniature coaxial cables may be used for better signal integrity.
https://68kmla.org/bb/index.php?threads/has-someone-the-db15-db15-video-cable-pinout.31010/ claims the apple high resoloution color monitor needs a cable that is straight through wired with all 15 pins present but I have no way to validate this information.
* Wikipedia similarly pushes the use of the term 8P8C for what everyone calls RJ45.
** The 15 way being the only high density connector that is widely used.