I also own a '96 Blazer, and I have done this. It's actually easier on the older models than on the '98+ ones.
You should note that during '95-97, Blazers came with two different headlight styles: either the rectangular sealed-beam (you must replace the entire assembly) or composite (you only replace the bulbs). Since the composite assembly has the corner light and headlight housing integrated together, I think it's safe to assume yours is a sealed-beam assembly like mine. (I actually upgraded it by replacing the sealed assemblies altogether with a bulb conversion kit. To see how I did this, just visit www.blazerforum.com and run a search on my name, Psychropod.)
You must remove the grille. Sounds complicated, but it's really not. You can do this in only a few minutes. First, pop open the hood. There are six bolts: four across the top, and two in the middle, like this (each X represents a bolt location). The two middle ones are a little hard to find, but just look directly above and below the Chevy "bowtie" emblem and you'll see them.
------------X------------ <<<< grille
-------------------------- Sorry about the crude diagram, but I can't insert pix here.
Remove these six bolts, then the grille will pop right out. Just be careful when popping it out, because each corner light has wires attached, and you don't want to damage these. After gently setting the grille down onto the bumper, you can then twist each corner bulb assembly out of the grille, then pop out the old bulb and pop in the new one. Then gently put each bulb assembly back into the grille, pop the grille back on, tighten the bolts, and you're done.
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