The running in of either loom is the same.
The later loom being for LHD isn't a problem as such, more of an inconvenience.
If you have a soldering gun and a few metre's of suitable wiring to extend three wires, along with an hour of your time then it'd make the loom good for RHD.
Although being able to use an earlier loom would save you doing this and would be the easiest route to take.