Black Hammer is defined as program that can have a Psychotropic program option, ergo from the description of Black Hammer, the limitations of Black Hammer apply.
first of all, the limitations to black hammer only apply to black hammer. secondly, black hammer can still do damage to cold sim users, it's just that it deals stun instead of physical. damage is still dealt, therefore psychotropic option kicks in.
and secondly, you're gonna have to come up with a better similarity than 'they both use ASIST'. a smartlink and a simchip with the latest karl kombatmage both use ASIST, but that doesn't mean i can slot karl kombatmage and get +2 bonus dice on certain firearms tests.