First, check the "contacs" tab on any station, more than half of them has "black market" option, thats where you sell this cargo. Also, do not worry about the authorities, if you master your docking manouver enough, you can get from the jump exit to the mailbox quiet fast- if you see that you are being scanned, just switch to the silent run mode (backspace key is default) which stops the scanning. Tricky part is that you pile the heat up, but if you turn the silent mode off after you get through the mailbox, you can switch the silent mode on and your safe... Also, dont forget that silent running drops your shields, so you cant bounce the entrance, or the landing pad. Anyhow, this method has never failed me, even in the high security systems.
I discovered it, when i was interdicted by a pirate in ASP, while having a full superconductor load, we had a cool fight, but those pesky authorities came to help me, i accidentally hit one of them with my wild beam laser, i got a bounty on my head and 3 vipers shoting me... I run away with 45% of hull left, no money for the insurance (superconductors are not cheap) and i realized that i have a bounty on me when docking the station... It started to scan me and in desperation i turned the silent mode on: i couls land without any problems... Actually there was no black market, so i sold 1 superconductor to repair my ship and went to another station in the same system. Docked again, also turning the silent mode at the scan attempt, worked again... Ive done this several times now...