Proper way to lubricate speedometer cable

[92470]

I have a 87' V10 and my speedometer is bouncy from a stop up until about 35 mph. After that, it levels out but still moves a bit. I want to pull out the cable to clean and grease it, but was wondering if the best way is to pull it out from the cluster end, or the transmission end? I made the stupid mistake of removing my TV cable one time and had the Old Faithful of tranmission fluid come pouring out, so removing anything from a tranny when full scares me. So, best end to remove it from, will tranny fluid come out if removed from that end, and any other caveats with doing it. I'm also going to use PB Blaster Garage door Lube. Had good luck with that stuff. Thanks!