These are SMD caps (the others are called "hole-thru").
Just get quality replacement caps , clean the pads on the pcb and apply a thin layer of fresh solder on them. Then place the new capacitor in it's position, put some solder on your iron't tip and heat the new solder on the pads (touch the cap's "legs" as well) so everything gets soldered into place.
Use lots of flux 😁 and don't spend too much time heating the pad else you risk lifting it and making the repair job more difficult...
edit:
watch this vid, it's shows what I am trying to explain: https://www.youtube.com/watch?v=EXw4tdxIAPA
In the video he does not re-solder the pads like I wrote above - I use this trick so the cap is easier to solder, just do whatever you find easier, it's the same result 😉