First of all it's not clear from your question whether you want to make the disk thin or not? Quick Migartion allows you to choose the relocated disk type
(it uses thin disk by default).
The disk is already thin provisioned. However, the disk has grown unnecessarily because we had out of control shadow copies at one point, so the disk has effectively become thick provisioned with alot of white space. I was wondering if I could essentially shrink the underlying VMDK easily using quick migration rather than using alternative methods (i.e. sdelete). So the question is, will quick migration skip this white space?