One fun option when hiring a singer is to hire a professional imitator. While most people are familiar with Elvis imitators, there are also plenty of Tom Jones, Cher, Barbra Streisand, and Madonna imitators out there, not to mention hordes of others.
If you've got a singer in mind, be sure you attend one of their performances before you hire them. Even if you can't swing a free seat, you should be willing to pay for the performance. Small live music venues rarely cost more than $20 or so a ticket, which is much less than you'll be paying your performer.