Replacing rivets can be a difficult process, even with access to both ends of the rivets. They were generally driven in hot so that they would deform to fit the holes tightly, even if the plates weren't completely aligned. Consequently, they often times cannot be driven out, and instead must be drilled oversize to remove all of the rivet.
Even if the steel is weldable, if the the plan is to keep the bridge is service, the fracture toughness of the original steel must be considered for fatigue resistance, and it wasn't typically very good. Bolted cover plates could work.
Unless the corrosion is fairly isolated, it will likely be more cost-effective to replicate the bridge using modern steel, and put the original on display somewhere.
Rod Smith, P.E., The artist formerly known as HotRod10