If you keep the new Win7 drive set first hard drive to boot in BIOS setup, then it should have no effect on your system to plug back in the old Win7 drive.
Just boot into BIOS setup immediately after you plug it back in to confirm boot order is correct, then reboot into your new Win7 to you should be able access your data in Explorer to copy onto the new drive, or isolate it on a partition on the old drive so that when ready you can correctly delete the old Win7 32 bit partition in Disk mgmt. - the correct way to delete an OS. We can help you with any of this jiu jitsu as we do all the time here.
If the old HD does not show up in Win7 then make sure in Disk Mgmt it has its drive letter, or rightclick the drive to Add one.
As long as the new Win7 drive remains set first to boot, you can keep the old Win7 32 bit for up to 30 days when you must activate the new one with its Product Key - unless you have another Product Key to use in which case you can keep both, choosing which to boot via the BIOS. If you don't like BIOS boot though, we can help you configure a Windows Boot menu using EasyBCD.