I would assume if the aircraft is going westbound there are two ways, N reg it first and take advantage of the fact it has been done before and use the STC's or the other option is to crate it over by boat.
I do stand to take critisism as I've been out of the loop for 8 years now in the industry.
It depends what tanks it has fitted, I cannot recollect if the 182 can with "long" tank installation as an option, either USA or Reims variants.
Duchess Driver has provided a sensible route there, however who who want to to an aircraft with no de-ice capaility at any point let alone across the pond at this time of year? Sense would say unscrew her and crate her over.