What should I do if I want to send my coins to the exchange after upgrade the public key? The addresses on the exchange have not been updated yet.
Just use the conversion tool until the exchanges upgrade to the new wallet. Then I assume your wallet will reflect the new prefix. They are interchangeable. Here is a demo of the new wallet with the new address being used. This was shared on Telegram by Bitcore team.
https://www.dropbox.com/s/97dj9yeymblt1id/Bitcore%20v.0.15.1.0%20Legacy%20Transaction%20Demo.mp4?dl=0