A couple of things I think are missing, as I'm not seeing them. Page 4-53 in your owners manual breaks down your actual towing capacity. A Yukon XL with 4:10 gears and 2Wd with 5.3 V8 is the one equipped to have an 8800# tow rating. Are you sure this is your truck? I suggest before you proceed you do a bit more research and validate what you really have. If it's 4WD with 3.73 gears, you are down to 7,600 lbs capacity.
You can find out your gear ratio by cross referencing the RPO code in the glove box.
3.42 = GU6
3.73 = GT4
4.10 = GT5
4.10 is pretty rare. 3.73 is very common.
https://my.gmc.com/content/dam/gmownercenter/gmna/dynamic/manuals/2001/gmc/yukon/2001_gmc_yukon_owners.pdfEither way I think the 6400# trailer should be just fine. With an XL I would not worry about sway. Watch the payload, and just make sure it's setup correctly, which you should with any rig.