Making new shoe string straps can be challenging, so there is a quick and easy way. Buy yourself some Rats-tail Binding. It is basically a very thin shoestring strap all ready made for you. Then all you need to do is attach it onto the garment. I have only seen it in a color black, but I am sure you can get it in other colors. It costs around A$4.00 a meter.
If you can't get any ratstail, find some fabric that suits the dress and cut your straps on the bias. Fold the fabric in half and sew 1/8th of an inch from the fold. Cut 1/8th of an inch from the seam and use a turner to pull the strap in on itself. You can buy a unit that allows you to push the strap through, but I find using a turner works well.
Happy sewing
Judith aka genie