If I search my deck for an Item and a Fighting Pokemon with Korrina, can I just take one if I don't have the other?
Yes. Do as much as you can. However, remember that you can fail any deck search for a specific card or type of card voluntarily.
Source: Furious Fists FAQ (2014-08-28), TPCi Rules Team (2014-08-28)

Relevant cards

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