First we're glad you asked. But we do need more information. The 9500# is probably a "best case" with a 6.0 or 6.2 engine and Max Towing Package. You have a 5.3. At best I'm thinking your TC is more like 7500#. The hitch rating for GM 1/2 tons is 1000-1100# depending on the year. A 9500# trailer will far exceed that. Without more information I would say that the 6000# dry is too much. Look for something that has no more than a 6000# GVWR. But again, that's a guess and guessing isn't a good idea with this stuff.
You need to learn everything you can about your truck's specs to get an accurate feel for what it can and can't do. Check your owners manual for the towing chart. The manual has a towing capacity chart listing the various available combinations of cab style, bed length, gearing, and engines. It also lists the GCWR, which is the max total your truck, trailer, people, and "stuff" can weigh.
Chevy Owners manuals. The ratings and option packages are the same as the GMCs. I can't find a link to older GMC manuals.
To cross reference things you also need to know your RPO codes. They are on a sticker in your glove box. These are just a few relavant RPO codes.
K5L = HD Cooling Pkg
NHT = Max Trailering Pkg
GU5 = 3.23 gears
GU6 = 3.42
GT4 = 3.73
GM RPO Codes