I think the player should be capable of voltage detection and should work but I would read up on that and make sure.
I would either bring the discs in your luggage or ship them. A collection that size would be easy to move if you abandon the packaging but I guess you don't want to consider that because they are limited editions. You could take the discs and ship the packaging separately. Three of these would make your collection fit in a luggage.
I won't address the backup question apart from saying if I was going to I would suggest the LG UB40N. Making disc backups is no longer something I find worthwhile but you have to make your own decisions.