Newsflash my friend, candidates always have a number in mind, even if they're not sharing it. By disclosing only your lower bound rather than the full range of your compensation, I'm pretty sure you're doing yourself a disservice. When people apply for a position at one company, they're probably also interviewing at 10 others. A good engineer that seemed (to you) unsure about comp will eventually pass the first round at places that are more transparent with a number that hits your undisclosed upper range (just the fact that such places exist should hint at something wrong about your beliefs). That'll then solidify a ballpark figure for that candidate. Guess what happens then. At best, your lower bid puts you in a low priority pile. At worst, if you're then willing to revise that number when the candidate later tells you it's too low, you look like a company with a culture of trying to lowball engineers.

Instead of being cagey about comp, do your own homework. Determine how much filling the role is worth (which should also include cost of keeping it vacant). Disclose a range to candidates. Evaluate them for your needs and determine what you're willing to compensate them based on your own estimation of their competence. If there's a mismatch between their expectations and yours, that's where negotiations should begin.

Not overpaying for a role if you don't have to? How much is "overpaying"? You're a business, so shop like one. Don't play games with nickel and dime accounting. Put a number on resources. Acquire them and move it to expenses. Then go back to getting things done.