I finally managed to get a hit on Newspapers.com. A full page Kroger add in the Tuesday, September 13, 1994, Paris News, from Paris, Texas, mentions the stickers. That week's stickers were listed as Troy Aikman, Darren Woodson and Erik Williams. I will see if there was a weekly ad in the Paris News and post the names for each week as I find them. The dates are just the days I found the ad in the paper. The stickers were usually just available for that week.
Week 1 - 13 Sep - Troy Aikman, Darren Woodson, Erik Williams
Week 2 - 21 Sep - Emmitt Smith, James Washington, Mark Stepnoski
Week 3 - 28 Sep - Michael Irvin, Kenny Gant, Tony Tolbert
Week 4 - 4? Oct - Daryl Johnston, Kevin Williams, Leon Lett
Week 5 - 11? Oct - Nate Newton, Shante Carver, Charles Haley
Week 6 - 18? Oct - Russell Maryland, Marl Tuinei, Kevin Smith
Week 7 - 25 Oct - Alvin Harper, Willie Jackson, Jay Novacek
I didn't find actual ads naming the players for Weeks 4-6, but eBay listings lined up with what I'd found in the papers, so I think this is the complete set. I found references to these as far north as Parsons, Kansas.