You say you held your ticket "through Aerosvit Airlines's website". This website has an FAQ section.
Question 6 of the FAQ reads, "May I change or cancel my reservation / e-ticket online?". The answer ends with,
Presently you can not change or delete Your online bookings in the online mode on Your own.
In case of finding out an error, assumed at booking, immediately report to Online Sales Group: firstname.lastname@example.org.
Changes or refund are made without any fees – if the request about an error is reported within 12 hours of the booking date after the online booking was made.
For the rebooking questions please contact Call Center 0 800 509 800, (+38044) 4903490 or the nearest aircompany office.
You can fill in the form "To rebook or to refuse the electronic ticket".
Live Chat service will allow you to change the details of your electronic airline ticket and, if it is required by the fare rules, to pay in the Internet with credit card.
So I think this is the best way to proceed.
The first question in the FAQ is, "How to book and purchase the tickets online?" The answer includes these instructions:
If You are not currently willing to pay for the ticket online with card, You can pre-book a flight and pay for it within 72 hours. Option for you - "Pay later". You will also receive notification on your e-mail with details of your trip and information about exact time, when you need to buy your ticket .
Advance booking must be completed at least 5 days before departure. The ticket price will remain the same as it was at the booking time.
That implies pretty strongly to me that if you do nothing, the airline will drop your reservation, and you will not be charged.