In Unlimited, can I use Korrina to get old Trainer cards like Professor Oak, Item Finder, etc.?
Yes. If a card is not a Supporter or a Stadium card, it would be considered an Item card by a new card effect.
Source: TPCi Rules Team (2014-09-04)

Relevant cards

Note: All applicable cards may not be listed below.
XY3_111
XY3_95