I found the connector. Look for "NDSL touch screen ribbon port socket" on Ali Express. At the time of this writing,10 pieces for $4.01 with $2 shipping to the US. Make sure you buy at least a handful, and it helps to use a digital microscope.
I removed the solder temperature. What settings you should use will vary depending upon your situation. Desoldering the speakers is not very difficult at all, provided that you use flux, and many different techniques should work.
I have updated the guide thanks to all of your feedback. If you've mastered these steps, then you can graduate to disassembling almost any Nintendo handheld. The one that I've had the most trouble with is the new 3DS XL. Newer and older models, including the Switch, are not much more difficult than the DS Lite, except the ribbon cables. They can be a real challenge.
Definitely do be careful. The digitizer is almost always worn out on the DS Lite, though, and it is a common repair. See step 8 for the recommended way to lift the locking tab using a small flathead bit.
Hi, Marcus, you're no doubt looking at this picture in isolation. If you had a console in front of you it would be more obvious: Use your fingernail to lift the ZIF locking tab. I recommend that you don't use a metal tool for this, but a high quality plastic spudger might work. The iFixit spudger is too thick for this.