I really like my duck bill applique scissors for trimming really close. Gingher's only makes righties, but there is a LH version available. Have to think of the name.
If the applique is not too too detailed, you can also hoop the applique fabric first. Stitch the outline. Take the fabric out of the hoop and cut right up to the stitch. Hoop background fabric, stitch the outline and use it as a placement for the applique fabric. Use washable school glue/glue stick to stick the applique down, then advance to the satin stitch.