A tad late, since you bought the corks, but you can also use plastic corks, which can be pushed in by hand.
One of the great disappointments of my brewing life is that some years ago, moving from apartment to apartment, I tossed or lost a floor corker which someone had given me. At the time, I don't think I knew what it was. Every now and then, I still look for that missing box that had the corker and some other long lost brewing equipment...