Here are the answers:
Drive by - James "Drive By" Washington from Compton, CA.
Woody - Darren "Woody" Woodson
Big E - Eric Williams
Hawk - Tony Dorsett actual nickname from high school, college and the Pros before TD.
Little Puddin - Walt Garrison - see Kskboys post
Catch 22 - promotional nickname for Emmitt Smith
Playmaker - Michael Irvin
Hollywood - Thomas "Hollywood" Henderson.
4 Irishmen and a Scott - John Fritzgerald, John Cooper, Tom Rafferty, Pat Donovan, and Herb Scott
Manster - Randy White
Too Tall - Ed "Too Tall" Jones
Beautiful - Harvey Martin
Cubby - Everson "Cubby" Walls
Thurman's Thieves - Everson Walls, Dennis Thurman, Mike Downs, and Benny Barnes 1981 originals
Thrill - Tony "Thrill" Hill
Fri-light - Alvin Harper - was "Highlight" but Cowboys players use to tease that he only made plays at Friday practice.
Tank - Demarcus "Tank" Lawrence
Captain Crash - Cliff Harris
Everybody's All American - Jason Witten (Parcells nickname for him)
LA - Larry Allen
Big Cat - Rayfield Wright
Black Unicorn - Martellus Bennett
Bambi - Lance Alworth
Clutch - Drew Pearson
Kitchen - Nate "the kitchen" Newton
Mr. Cowboy - Bob Lilly
TO - Terrell "Team Obliterator" Owens...kidding, I think?
Moose - Daryl "Moose" Johnston
Bullet - Bob Hayes
Prime Time - Deion Sanders
Jump up - Jimmy Johnson
T New - Terrence Newman
Killer - Lee Roy Jordan
Double Digit - Dat Nguyen - Actually "Double Digit Dat" from his double digit tackle games
Big Cat (the other one) - Leon Lett
Step - Mark Stepnoski
Gentle Giant - Mark Tuieni, President Obama's first body guard.
Hotel - Flozell "the hotel" Adams
K Dub - Kevin Williams
Big John - John Dutton
Big Nasty - Kevin Gogan
Sweet Lips - Cornell Green
Dandy - Don Meredith
Bubba - Larry Cole
Bowling Ball - Robert Newhouse
Last Naked Warrior - Charles Haley's self nickname other than crazy from everyone else.
Scoey - Emmitt Smith's real nickname
Dan - Danny White
Toast - Elvis "Toast" Patterson
Shark - Kenny Gant
Turkey - Bob Hayes actual team nickname
Iceman - Troy Aikman, high school and college
Roy - Troy Aikman also called "Roy Boy" by teammates.
Godfather - Troy Aikman
Dodger - Roger Staubach
Captain Comeback - Roger Staubach
Captain America - Roger Staubach
Bonus -
Stone Face - Tom Landry behind his back by players
Deuce Deuce - Emmitt Smith by some
America's Team - The Real Dallas Cowboys
Neon - Deion Sanders
Dirty Dozen - 1975 Draft Class and UDFA that made the team and went to the Super Bowl.
Martinize Em - Harvey Martin
Highlight - Alvin "Highlight" Harper
The Hammer - Ken Hamlin
The Intimidator - Charles Haley while in SF.
The Triplets - Aikman, Irvin, and Smith
Pup - Kevin Smith
Bully - Bill "the Bully" Bates
Bo - Herschel "Bo" Walker. Walker ran over "Bully", UGA fans called him Bulldozer. AKA "The Trade"
Rock - Dexter Coakley
Hitting Machine - Eugene Lockhart
Quincy - Lavonya Quintelle Carter...yes Quincy Carter
Superman - Roy Williams S
Biscuit - Roy Williams S by Parcells
Butch - Michael "Butch" Johnson
Godfather - Gil Brandt by NFL personnel people