It will drastically reduce the rattle, and most likely eliminate it completely. I've never tried to lubricate stabilizers without removing them though. If you're up for desoldering, I highly recommend removing the switch above the stabilizer, pulling out the stabilizer (easy to do on a pok3r b/c they are plate mounted), taking it apart to lubricate, reassembling, and then resoldering the switch.
Desoldering is the easiest way to ruin a PCB if you are a novice, so I'll offer a few tips.
Choose a decent soldering iron with temperature control and a chisel tip. You can read all around about what to get, but just make sure it's something a step up from local hardware and big-box store irons.
Put a bit of fresh solder on the joint before you try to remove the old solder. Alternatively, you can use flux, but some good rosin core solder is all you really need. That way you don't have to buy too many things to get started. I highly recommend 63/37 blend because it flows so easily. If you're worried about lead, just make sure to wash your hands after soldering. The cancerous stuff is generally the fumes from the heated flux.
https://www.amazon.com/gp/product/B00EDLR8TS (what I use)
Just a dab of fresh solder on the old will do. When you stick your 650-700 degree iron against solder and it doesn't "melt" it is most likely b/c it needs flux on it. The flux in the core of the new solder will help the older solder to "flow" (melt into a thinner puddle) once heated up. Speaking of flowing, you'll have to choose how to want to remove it.
Cheapest is probably a cooper braid.
https://www.amazon.com/NTE-Electronics-SW02-10-No-Clean-Solder/dp/B0195UVWJ8I removed all the switches from 3 60% boards using a braid. Also, I've ruined 3 pads on a pok3r PCB using a braid. Just have to avoid overheating (again, this is helped by adding flux or a dab of new rosin-core solder)
Next option is the solder sucker hand pump. The only way this becomes problematic is
if when you don't get all of the solder in the first pull. Then you're left with solder that is level to or below the pad that still needs to get sucked out. DON'T cram your soldering iron down in there to heat it up! Add solder back to the joint before you attempt to re-suck it out. You can put the tip on one side of the pad/pin and the pump tip against the other. You can even touch the solder tip to the tip of the pump and it won't melt.
https://www.amazon.com/Engineer-SS-02-Solder-Sucker/dp/B002MJMXD4I now have a desoldering tool that does the job effortlessly in seconds, but that's more in the $250 ballpark. I wouldn't recommend it for removing a joint here and there.
