-Get smooth jawed pliers.
-Bend the leads 90 degrees a couple MMs from the base off the cap.
-You should put heat shrink on the leads but not REALLY necessary unless it's close to another component.
-Bend the leads 90 degrees under the cap to mount them above or between the pads.
-Dab some hot glue on the bottom to help hold the cap down. Again, not REALLY necessary but if you're going to do it, might as well do it right.
You should know that your soldering isn't great, I'd recommend working on that. Thumbs up for using Nichicon caps.