The method fo removing solder through hole components; where you can access the component fully,
per my days in medical instrumentation, is to use fine wire cutters and cut the leads as close to the body of
The component as possible. Then remove the component. Next take a small pair of needle nose pliers grab the lead and heat the pad using a tip with a drop of solder on it. When molten pull the lead out. Then reapply heat and use a solder sucker to clear the pad and through hole. This reduces the chances of damaging the feed through hole.
I am not a big fan of solder wick as it can often lead to overheating the pad and damaging it.
Also if you are having trouble getting a small piece of solder off a pad or feed through. Re-apply solder to the whole pad and feed through and then try the solder sucker again.