he has a 9" in that bronco.....no c-clips,the axles are retained by plates on the outer ends.
and while it is possible to weld spiders on most diffs without pulling the ring gear,i don't reccomend it.pull the carrier,remove the gear,clean the hell out of it with solvent(as noted-not brake clean)and weld the side gears to the carrier thoroughly.then,reassemble after it's had a chance to cool(slowly)
if you have a 9",the side gears are hidden inside a closed carrier that splits by removing the ring gear.spiders must be removed to get to the side gears.weld ONE side gear thoroughly,making sure not to damage the mating surfaces on the carrier halfs,then reassemble.
the reason for only welding one side is that it is almost impossible to align the side gears on the two carrier halfs so the spiders fit back in.
you could also just weld the two side gears and leave the spiders out,but i find the former method to be more effective.