Unfortunately, at least with these trucks a muffler/resonator change won't do much to help performance/gas mileage. At you just looking to cut out the old muffler, and have a new one welded in or do a full exhaust replacement? I know Walker offers a complete kit, or you can purchase just the muffler + resonator and have them cut/welded in. The Walker muffler is pretty much an OE replacement, so there won't be a noise increase.
If you're looking for gas mileage increases, a good highway tread tire with the least amount of rolling resistance will net you a tiny bit. Same goes for a tune (from Limeswap or PCM of NC) since you won't be laying into the throttle much to get her going. Otherwise, make sure the O2 sensors are operating within spec since that'll be another hit to MPG, and maybe a tune up/run some Redline fuel cleaner to help clear carbon build up.
Having been near a Trailblazer with both the resonator on and removed, especially on the I6 there wasn't much if any of a noise increase even under acceleration. The resonator is really just unneeded weight in the rear. Now if you had the V8, there would be a noticeable ton/noise output, same goes for the I6 if you slapped a Cherry, Magnaflow, Flowmaster, Borla or whatever then yeah the resonator would help tame the sound. I would just get the old one cut and removed, and let the resonator eventually rust off or get it removed and you'll be good!