Hello
NO, I believe you should not install windows on another machine and then swap harddrive.
you can do that on current "bad" machine without pulling HD out!
the better way would be so:
made two primary partitions on hardrive (first inactive, second active), then copy installation files onto second partition and restart.
that would start installation.
you'll of course install on first partition.
as soon as installation boot's up accept everything until your reach to the point of disk choice.
then press SHIFT+F10 to open cmd.
swap the active partition so that first(where windows will be installed) become active and other one inactive(where win installation files are).
(you'll do so using DISKPART)
now close cmd and hit F5 to rescan partitions.
finaly select empty(active/system) partition and start installation.
when windows boot's up(installation finishes) delete contents of D:\ partitioin where windows installation files are.
cheers!