Before you begin the job, get hold of BRAND NEW replacement sockets. Not just check they're available, but physically get them first!
Preferably get the decent ones with metal retaining clips.
Measure them to check they'll fit, and the pin placement and footprint is the same as the old ones.
All the pads are through hole plated. There are lots of internal tracks connected to the pads, so it's essential not to damage any.
2 ways to remove a SIMM socket:
1. Get a decent vacuum assisted desoldering gun, like a Hakko 808 with a NEW 1mm tip to remove the solder from each joint.
Make sure each pin is totally free before removing the whole socket.
Unless you know how to use the desoldering tool correctly, you risk causing pad damage, so be very careful.
2. Apply a little fresh solder to each of the socket pins. Using a conventional soldering iron, heat each pin one at a time, and as you do so, use needlenose pliers to gently pull the corresponding socket contact vertically upwards.
It's time consuming, but doesn't require special tools, and there's less risk of pad damage.