Leonard Susskind and Stephen Hawking both said that
if you had the right kind of BH (meaning right size and not active accretion)
you would happily cross the event horizon and not even know it.
I'm not familiar with that statement by Susskind and Hawking, but I'm pretty sure you've misinterpreted it. If "cross" means only passing near the black hole, and if it's small and not actively accreting, then that statement is correct; you may not realize you've passed it.
But you cannot actually cross through (in and out) of the event horizon. The event horizon is the distance at which the gravitational pull accelerates things towards the black hole at the speed of light. Producing an opposing equal acceleration to hold position is impractical, and a greater acceleration to escape is impossible.
So in classical physics terms ,what kind (size) of black hole do we need for the probe weight to be practical?
Subatomic. Anything larger would be shredded by gravitational shear forces before reaching the event horizon.
Even if that wasn't the case, a probe in the traditional sense would be useless, due to temporal effects near strong gravity wells. What kind of useful information can you transmit when the probe's 3 gigahertz processor, in its brief descent into expungement, looks to the rest of the universe like it's operating at 1 femtohertz?
But quantum entangled subatomic particles may be able to transmit some sort of information out.