Use of a Helping Hands is recommended to avoid soldering iron contact. If you do not have one, hold the board at an angle.

While a partial replacement may work, the remaining capacitors will fail. Change them all while it is apart. Refer to this guide for soldering tips: How To Solder and Desolder Connections.

Move to a workspace with ventilation or use a fume extractor. Once in an appropriate workspace, desolder the old capacitors. Heat up each leg and remove it.

After removing the capacitors, clean up the old solder with a desoldering braid. Lift it with the iron when removing it.