Exchange 2010 certificate issues

Noob Exchange Admin here.
Running Exchange 2010 SP3 and have an annoying certificate message poping up when you launch Outlook or access via OWA.
"Name on the security certificate is invalid or does not match the name of the site". Users click Proceed and all is well.
There are 2 certificates on this server. One is a Verisign cert with the name webmail.mydomain.com the other is an exchange certificate with the name ExchangeSrv. All services (IMAP,POP,IIS,SMTP) are assigned to the ExchangeSrv certificate.
Under Server Config in the Client Access group, OWA has internal and external URLs of https://webmail.mydomain.com/owa.
In the Exchange Control Panel config, I have an internal URL of https://exchangesrv.mydomain.com/ecp but the external URL is https://mail.mydomain.com/ecp.
My question is, can i move all the services to the Verisign webmail cert and remove the exchange without killing everyone's connection to the exchange server?
Also, would I need to change the ECP Urls to be webmail.mydomain.com?

About to migrate to Exchange 2016 standalone and want to make sure all my certs are properly configured before I start the migration.

Thanks for you input.