I have never seen a delta shirt. How many tags do they have? One or two? If one, then you'll need to make sure your new labels has the required information regarding the washing instructions and origin of the shirt.
If it has two labels, then hopefully the top one is the delta logo/size one, and the bottom one is the washing instructions/origin. You'll want to keep that 2nd label in and just remove the top one to replace with your custom label.
If you can't sew
, then you could try your local dry cleaners who does sewing repair. Expect to pay anywhere from .25 cents to $1 to have this done.
If that doesn't work, visit a couple of sewing center stores, and post a services needed post on their bulletin board. That's where all the seamstresses go.
Has anyone relabeled delta apparel. 
