I would applique it first and then stitch in the ditch. I have applique over many pieces of a log cabin old quilt to repair it and worked for me. It is my opinion anyways. Or you can try on a little space and see the result with your machine and skills.
Use the thinner cotton thread you can manage, and the color should be of the applique piece or silk thread if you could, sometimes silk is challenging because it tangles a lot.
good luck