So I can basically move the partition physically on the drive with this software?
Absolutely.
Is it safe to do this to an OS partition?
Absolutely.
What you didn't describe completely is how you installed the second OS on the second drive, while retaining the first OS on the first drive (and which you now want to slide to the left on the drive itself).
Normally, when installing a second OS, the Windows installer detects the presence of an existing bootable Windows and creates a Boot Manager Menu. This menu then appears when you boot the machine, providing you with a choice of which of the two OS's you want to boot to (one is normally set as the default, which typically is the most recently installed Windows). This Boot Manager Menu approach is very convenient for this exact functionality.
Alternatively, you can get into the BIOS (or SETUP) at boot time and manually pick a drive/OS you want to boot from. This is more clumsy than the easy-to-use Boot Manager Menu method normally used, but it will also work.
So... what did you do? How did you boot to either of your two Windows when you still had those original two partitions (D and E) which you've now deleted? I ask this because the Boot Manager Menu contains a physical partition number on the drive, for the bootable OS partition. So when you still had D and E on that drive (arranged D, C, E) the bootable C partition was partition #2, whereas now that you've deleted D and E it is partition #1. This would cause a problem for Boot Manager Menu, if you were using it.
Yes, you can slide your C partition to the left with Partition Wizard with no problem or consequence. But if you were using Boot Manager Menu, your deletion of D (originally to the left of C) has caused a renumbering of the partition C still on the drive, and this needs to be corrected. I would recommend that you
use EasyBCD to "repair" the Boot Manager Menu. You'd boot to your second/latest Windows, install EasyBCD, and then "edit the Boot Manager Menu" to add your now-slid-left C partition on the first drive as a second bootable OS.
EasyBCD is a very easy to use GUI maintenance tool for the Boot Manager Menu.