My preferred tip for a job like this is a knife tip:

https://www.hakko.com/english/tip_selection/type_k.html

Put lots of flux on the pins and drag solder like you're soldering a LQFP to a PCB. Just make sure you get rid of the flux when you're done.

It doesn't look like there's any non-washable parts on the motherboard so don't be afraid of giving it a good soak in alcohol.