Sometimes, and I say sometimes, the onlyway to remove the hardward is to 'move/remove' the sink itself.
Look up underneath and see if you see some retaining screws and clamps that hold the sink to the countertop. BEFORE you do anything, envision if you could do what you need to do by simply loosening the clamps and 'sliding' the sink one way or another. (Oh, I forgot, I'm assuming you have flexible feeds, but maybe you can still do it. Just 'imagine' ...) Anyways, after you do this, USE flexible lines when you reinstall. You may ALSO need to seal up around the sink. It's done a couple of different ways. Maybe what you might want to do is let us know more about the feed-lines, the type of sink, countertop, and how it's all 'clamped' down. From there, we can tell you what you need to do.
For now, my best to ya and hope this helps.
Jay J -Moderator
PS: If you know any plumbers or any 'experienced' DIYers, or any friends of friends that are plumbers, try those sources for information. If you can find someone that's a plumber and is looking for a few $$$, just tell them you need them to 'loosen and remove' the old fixture first. THEN, once you get him inside, pump him for info on the reinstall.