the time of the wait

[sunsunmoon]

Put the customer on hold only if it is absolutely necessary. No one likes to be left on hold indefinitely. If you must put a customer on hold, estimate the time of the wait and ask whether he or she would mind holding. If you do have a caller on hold, check in with the caller every 45 to 60 seconds. A minute is a lifetime when you are on hold.
(From http://www.ehow.com/way_5749408_techniques-effective-telephone-communication.html)

Does the time of the wait sound natural to you? Would "the wait time" be correct?

[emsr2d2]

Put the customer on hold only if it is absolutely necessary. No one likes to be left on hold indefinitely. If you must put a customer on hold, estimate the time of the wait and ask whether he or she would mind holding. If you do have a caller on hold, check in with the caller every 45 to 60 seconds. A minute is a lifetime when you are on hold.
(From http://www.ehow.com/way_5749408_techniques-effective-telephone-communication.html)

Does the time of the wait sound natural to you? Would "the wait time" be correct?

The original is fine.

[sunsunmoon]

Would it be incorrect to say estimate the wait time instead?

[Rover_KE]

No.