Is there a way to copy everything on our current hard drive (Windows Server 2008 R2) to an SSD drive and just swap it out with out an hitches?

You are an optimistic soul!
There are easier ways and harder ways, but for the highest success factor/lowest frustration factor, I recommend Acronis Backup & Recovery. It does the best of any of the tools we have used recently for moving between dis-similar hardware. We use it primarily for bare-metal restores to dis-similar hardware, or P2V (Physical to Virtual) transitions.
It is also a great tool for running multiple scheduled backups for the professionally paranoid.
It is available in the channel, let me know if you decide you need additional help.