The only stats that is hinted to make an effect on wasteland exploration is Luck and Endurance. There is a few other hints that SPECIAL stats make an effect on exploration but no details is given. So this dude in the below link made a study.
http://www.gamefaqs.com/boards/168521-fallout-shelter/72446315
According to it the only specials that make any effect on exploration is Endurance which raises survival time and luck which gives you more money but not more or rarer items. I am really pissed that I read this study after I have leveled my 8 dwellers with nearly 10 in every stat and nearly level 50 all. It took days and I have seen now with a statistical anolysis it is shown that I have done nothing.
Every special should effect wasteland exploration in some way.
For ex:
Strength : There should be carry limit and strength should increase it. Also should increase run speed cutting making exploration faster.
Perception: Better damage with guns. Better at killing things. And better at spotting items. Should increase the chance to find more and better items.
Endurance: Already raises HP.
Charisma: Finding Dwellers in wasteland. (Rare or generic leveled. Also luck should affect this)
Intelligence: Rather than I stabbed the mirelurk in the face where he has no armor be a generic text they should be specific to high intelligence in the long run less damage during exploration.
Agility: Gives a chance to dodge attacks.
Luck: Already is affecting. But should also effect the quality of dwellers found in wasteland that charisma provides.