The contingency agreement the med malpractice attorney puts in front of you will be several pages long and complex. At the end it will say something like "We cannot act as your counsel in negotiating with this firm. You acknowledge that you have used your own independant counsel in negotiating this agreement." This means, "although we hope you won't do it, we advise you to hire an attorney to review this in order to cover our asses when you complain about the terms later on."
So, read the contract word for word, and seriously consider hiring a contract attorney familiar with the going rates for contingency fees to review it and explain it to you. He may or may not be able to negotiate better term (often, he will be able to do so), but at least he will be able to tell you what it says and what the risks are. You'll probably spend $300 to $500 for this, but it's worth it. Don't worry, they won't be offended.
For what it's worth, I think that is an excellent suggestion. If you are just paying the contract lawyer for his/her time without regard to the advice, you can feel more confident that the advice isn't influenced by potential payment, since the hours spent are the same regardless of the advice rendered. The only other caveat I'd say is don't hesitate to see more than one attorney. While no doubt it will be very difficult for you to go over the story more than once, you probably will learn something from each and after seeing more than one attorney, will have a much better basis from which to select counsel.