I'm thinking it can't be bigger than 1" but, it's been a while since I replaced mine. If you don't have a socket big enough to remove that bolt, you surely will need some tools if you plan on working on the truck at all.
For this particullar job anyway you'll need the correct size socket (of course)(you can use a ruler to measure across the head - go flat to flat and whatever it measures is the size you'll need), then a 4 - 6" extension, a breaker bar and a cheater pipe. Mine were so rusted/seized in there I had to bounce all 200# on the cheater pipe to "pop" the pass side loose. I had to wrap the cheater pipe with a towel on the driver side so as not to dent the wheelwell when the bolt popped loose, this side I had to use legs like doing squats to get it to pop. This was even after soaking with PB Blaster the night before and just before the job. I was lucky to have an electric impact to help spin the bolts out once loose. The bottoms were by far the worse. I actually bought new bolts because the bolts were worn from the shock beating on it due to improper tightening when previously installed. I used a washer to shim between the sleeve on the bottom of the shock and one of the tabs that the bolt pinches when you tighten it. Be sure to tighten the bejezzes out of the bottom bolt and check to be sure the bottom of the shock doesn't wiggle loose between the pinch tabs by inserting a big screwdriver or prybar between the outside edge of the shock and spring perch. DC used coarse thread instead of fine thread - DUH! Good luck.
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