Nice smuggling effort. I routinely approach and dock in FA Off just to practice and improve the skills... you don't need to be smuggling or in stealth to do it and as the FA Off flight is probably the hardest part of smuggling it's worth doing as often as possible so that when you need it you don't have to think about how to go about it. It's not only useful for smugglers, but also bounty hunters and pirates who have the opportunity to score cargo that's "fallen off the back of a hauler", or even traders who find "questionable" containers floating around freely in space occasionally.
Here's how I go about it... when I drop out of SC I locate the station's entrance (easier with orbital and oneill stations, slightly trickier with coriolis ones) and aim the ship on a line so I'll end up about 1km outside the entrance. FA Off and boost then throttle to zero. Select the station as my target so I get accurate distance readings from it (and so it shows up on the target hologram to make it easier to find the entrance and align with it), then I rotate the ship so I'll be facing the right way when I get to the station, then I just sit and wait till I'm 7km from it and request docking. As I'm flying sideways I just look at the "space dust" to determine which way I'm actually heading. Once I'm close to the entrance I start using manoeuvring thrusters to slow the sideways movement and the throttle to start moving forward till I'm nicely in line with the entrance. You have to remember not to leave the throttle on max or you'll end up moving super fast, so I just use "bursts" of throttle similar to the bursts of thruster to control your sideways motion, and bursts of rotation to get the ship rotating in sync with the station. Then I just ease thru the slot, watching the scanner for inconvenient Anacondas or type 9's who may decide to depart as I'm arriving and ruin my day. Once I'm inside I generally switch flight assist back on and pilot normally to the pad rather than trusting my FA Off skills inside the station.
Once you can do that without breaking a sweat then start working on your heat management skills at the same time to keep your cockpit iced up, and consider investing in a heatsink launcher as a quick way to drop your temperature to avoid scans. I used it with the stealth mode to do the "smuggling" thing for the first time yesterday as I'd been doing a bit of bounty hunting in my Viper and some NPC in an type 9 dropped a bunch of battle weapons for me and ran away... of course I don't approve of piracy, but I can't just leave dangerous weapons floating around space so I was obliged to bring them inside, for the safety of all of course!

The pilot in that video's using a Track IR, I use a home made ED Tracker (search for the threads on here), and I can really recommend them as a very intuitive way of keeping visual track of what's going on around you.
Another smuggling tactic is to not use the "safe disengage" feature of SC... you can slow your SC right down to 30km/s as you do the last 150km approach to the station and watch the distance carefully. "Safe disengage" only works between 1000-20km from your target, so if you can wait till you're less than 20km away you'll be dropped MUCH closer to the station (careful, sometimes it buries you inside the station's superstructure. You CAN get out of it, but better have 4 pips in your shields!). This can greatly reduce the amount of time you spend approaching the station, which equates to a greatly reduced time in which you can be scanned. Drop a heatsink as soon as you drop out of SC, hit silent running, and request docking as you locate the entrance (use the hologram to help you orient yourself) and you can be inside and docked in less than a minute from dropping out of cruise, with the security forces being none the wiser. If you DO get scanned aim away from the station (and the vipers) hit FA Off and boost, and jump to cruise as quick as you can, then try again. Remember they have to be within 1km from you to scan you and it takes them about 30 seconds to get a result so speed and distance are your friends here.