Ve-r-r-ry fast, if you know the law!
It's truly amazing how many employer lawyers attempt to use the ancient statute of frauds to shoehorn a contingency-fee arrangement into a contract that must be in writing and signed by the party to be charged (the client).
The common law (original judge-made law) evolved into written statutes that require real estate contracts, promises to pay someone else's debts, or contracts for larger sales of goods to be in writing. It makes perfect sense. Requiring a writing protects the parties against being defrauded (or just misled – whether intentionally or otherwise) by each other.
But there's another traditional area where the statute of frauds is applied. That is in contracts requiring more than one year to perform. Again, it makes perfect sense. If it takes a long time to perform a contract, the parties might forget the original terms.
Does a placement take more than one year to perform? Of course, one can. But this is the exception, and surely not within the contemplation of the parties. Oral contingency-fee placement agreements are fully enforceable . . . as long as you can prove they were made.
So don't let some employer lawyer ever fool you with this one!