I don't do the commish stuff for our league any more, but I did for a while. Here's what I recall...
We had it set up so that all players after the weekend games were on waivers. You could put in a claim Tuesday and waivers would run early Wed. morning (1:00 a.m. ET) to process those claims.
Any unclaimed player would become a free agent, available for pickup at any time, first come first serve.
Any dropped player, at any time during the week was put on waivers for at least 24 hours. You could put in a claim for that player and the next time the waivers process ran, your claim would be processed (along with everyone else's).
To accomplish this, the waivers process was set to run every night during the week (Wed morning through Sun morning) all at around 1:00 a.m. Free Agents do not get processed in the waiver system.
If your dropped players immediately become free agents, then you probably don't need to run waivers all week, just Tuesday night.
Hope that helps.