If you handle it like that (which is the same way I do it), it doesn't make much of a difference, if you bill hourly vs. daily, does it? The maximum of money your're going to lose out on, is the few hours of rounding up to a day, which with any significant client are going to be peanuts compared to the rest.
Daily/weekly are billing increments, not working increments. I still track hours internally; I billed a client last year for "one day" of work that took me a week due to other commitments. Made it clear up front that I was pretty busy at the time. He had no issues with it.