For the time involved with moving the app versus uninstalling/reinstalling, I would think the latter the better option. I have never heard of a successful move. I suppose it’s possible, but Office is such a large app there must be thousands of things to move. If the move is partially completed, then falters you are left with office 2010 kind of on 2 partitions and then who knows if the uninstall will work for either. You might end up reinstalling then uninstalling on both before an installation on C is possible.
My choice would be uninstall on D, run CCleaner registry cleaner on D to look for leftovers, then installing on the C Drive. I have never found a problem with reinstalling my Office 2010 as far as activation. I installed it on Win 7, then Win 8 RP then Win 8 Ent Eval, and now on Win 8 Pro with no problems with activation. These installations were in 2 different partitions.