Dear Dave: I'm working toward eliminating the credit cards used by my company. How do you get debit cards for employees that won't give them access to company bank accounts?
You don't. The debit card is what gives them access to the company bank account.
At my company, we run an operating account that several of my team members can access with a debit card. I look at it this way: If you trust your employees enough to travel and do business in your name and on your behalf, then you've got to be able to trust them with money.
If you think you can't trust someone, then don't send them out to do business for you. Better yet, don't hire them in the first place!