I usually mow my lawn on the highest setting on my mower so there's not much I can do when it grows too high. Don't worry too much about it if it's not something you do frequently. Sometimes life or weather gets in the way. The grass will recover if it's otherwise well cared for, fed, watered and gets good sun.
When you cut the grass it loses some of its ability to photosynthesize. When you give it a drastic cut root growth slows or stops temporarily and carbohydrates stored in the plant are used to produce new leaf growth. If you cut like this repeatedly you can use up all the carbohydrate reserves. Doing it once in a while isn't going to cause much damage.
But to answer your question.. Depends on various factors but 2-4 days should be fine. Aim to do 3 cuts to get down to the final height since the grass will grow some in between mowings. The tip of the grass at the cut will brown out a little and seal the end like a scab on a cut. Wait at least one day after that.
When you cut your grass the tear at the top causes it to lose moisture faster. If you're using a rotary mower the tearing is worse than if you're using a reel mower but I'm not aware of many reel mowers that can cut at 4.5". It would be beneficial if your blade is sharp to get a cleaner cut. There's lots of info on how to sharpen a mower blade so I won't go into that here but I do want to add before doing anything under your mower or near the blade disconnect the spark plug wire.
If you could cut the second time with a reel mower that would be better.
Try to avoid mowing if the weather is above 90 degrees to reduce moisture loss.