We have very high wire volume for our size.
Our controls are similar to Happy's. Our agreement allows anyone to be authorized to transact wires as long as they are on the wire agreement (with specific capabailities listed - maximum amount, repetitive only or free form, origination and/or call back, dual control, etc). The wire agreement also lists email addresses and direct phone numbers for each of these individuals, which allows wire staff to identify whether emails received are at least from a valid address (still not indiciating validity of the request of course). The phone number on the agreement or in the core system is the only number used to call them. The wire agreement must be executed by an authorized signer on the account, and their written consent is required to add users or change capabilities of existing users authorized to transact wires. We have passphrases set up by the users to identify them whether they call in or we originate call back.
Unlike Happy, we have not had an issue with allowing those individuals to transaction branch business. Authorized signers are listed as such on our core system. People only authorized to transact wires are not. Wire information (authorized transactors and passphrases) is stored on a separate system that is only accessible by operational staff (not the front line).