
You could bend the pins of this header outwards, then solder it to the diode pins.
Bend the small part, and be very careful as these tend to break off while trying to do that.
You can also bend the pin at each side of the diode twice to create an oval like shape.
Then cut the wires where they touch each other, leaving an opening of the same size as the width between the pins of your header.
Solder the wires to the part of the diode wires which are now perpendicular to the diode itself.
Soldering takes practising, so keep doing that.
And use tools for what they are intended to do.
Do not use your soldering iron to cut through plastic stuff, and do not use it to remove insulation from wires.
The tip of the iron will be eaten away by that nasty stuff, you know what that looks like.