Hi LJT90 and welcome to Kyiv forum :)
Independence Square is THE city centre. So it's very unlikely there are no taxis in the area - either driving by or standing by (those standing by the "hot spots" like hotels, restaurants etc normally overcharge).
So you may end your city tour somewhere in the centre and take a cab from there.
If you plan to eat out in the city before departing, you could ask the waiter to call a taxi for you. In this case better don't leave it to the very last minute - ask your waiter in advance to call a taxi for you for the specified time.
Finally, you could always ask your hotel to arrange a taxi for you for the specified time; especially if you anyway plan to leave your luggage in the hotel after you check-out, so that you don't have to carry it while getting around.
P.S. Make sure to let the driver know which exactly airport you need, and which terminal. Btw get ready that taxi drivers in Kyiv don't speak much English (if any).
If you need to get to the airport in the week-day and especially in the rush hour, add possible traffic jams to the time estimations.
Edited: 12:06 pm, February 08, 2013