If you want to make your life very easy, get some low melt solder. It's pricey, but you don't need much. Add some of that to the hole, then heat it up and use wick to remove it / clean the hole.
The issue will be that these holes are likely connected to internal and possibly external GND layers that are absorbing a lot of heat. If you don't have a good iron that can maintain temperature, you will have this issue.
As someone else said, there are many, many different ways to skin this cat (de-solder gun, de-solder pump, heating with hot air & iron simultanously, using a needle / toothpick, etc, etc). However, by far the easiest is to reduce the melting point of the solder so that the wick can readily absorb it before it cools down and hardens.
As such, some low melt solder will do the job just nicely.