You won't be able to do an "in place" upgrade of the OS to 64-bit as it's not supported, so it will have to be a clean install. I'm assuming you'll run the 64-bit version of whatever database software you're using, as well?
This migration guide should give some pointers
So very basically;
- Back everything up
- Install new 64-bit OS
- Install DB application
- Install WHD (same version as currently running)
- Restore database and run everything up
- Upgrade WHD
Would no doubt be best to contact Solarwinds support, as there may be some issues with paths going from 32-bit to 64-bit OS.