​Quietly fire an employee

I’ve caught an employee inflating hours and mileage. They don’t know that I know, I’ve been watching for a while to make sure that it wasn’t just a mistake.

I want to fire them without having a direct conflict over why because it’ll just end up in a useless debate and excuses and drama that I’m not interested in having. I just want to end this as drama free as possible. I’m thinking of saying business is slow and I just don’t have the hours available or something like that. Any advice appreciated.

They are an hourly employee who’s been with me roughly 2 months.