Depending on how hard the remaining material is, riveting may not be an option.
I am the son of depression era parents. I understand the whole thing about buy it new, where it out, make it do or do without. But, at some point, your time has to be more valuable than trying to resurrect three busted knives. Decent paring knives can be had for as little as $5 each, less on sale.
Good luck,
Kevin