and this is the sprayer I am using which is another reason the grass can't be too tall.

Here is a link that might be useful: Earthway sprayer

If you do need to spray poisons then you want the target plants to have enough leaf surface to absorb as much of that poison as possible. How soon after mowing to spray depends, then, on how soon the plants grow back enough and that is not something that is easy to state.
Much easier is to state that you should not mow for about 48 hours after spraying.