Remove the users from the BES first, that will ask if you want to remove the Blackberry properties from the mailboxes. Once you do that, you can move the users without any issues.
Is your BES working right now? We had trouble after installing 2010, our BES stopped communicating with the handhelds. We were forced to upgrade BES from 4x to 5x Express. Once we had BES5x installed, we used the Blackberry transporter to migrate the users from BES4 database to BES5 database. After that, everything started behaving fine.
Anyhow, assuming your BES is actually working, you can remove the users from the BES, remove the BES properties from the mailbox, uninstall BES. Any time after you remove the users from the bes, you can move the mailboxes to your 2010 server.
After you uninstall BES, you can perform the steps necessary to remove your final exchange 2003 server from the domain.