If you are SURE of the dye or stain used, you should have no problems. Occasionally when I have taken off a patch of finish and re-stained, the stain will leave a slightly darker ring at the edges of the clear coat I didn't sand off. Mostly, just really do a great job with the sanding in that area because the difference between a good and a mediocre sanding job WILL show up under the finish.
If you can, also figure out what the varnish or clear coat finish was. A lot of fiberglass bowyers use a 2 part spray on epoxy, some big operations even use UV-cured epoxy like flooring boards get. It's kind of hard to reproduce the look exactly. Any durable finish will work, but may no look exactly the same. You can even just use actual epoxy (like 2-ton stuff from wherever) and smooth it on if the patch is small. It goes on thick and leaves you with more sanding and steel wool work, but it looks fine.
BTW, this forum i really intended for guys who are in to primitive bows, selfbows, all-wood bows and hi8storical composites. You are CERTAINLY welcome to hang around, but if you need a place to go with questions about fiberglass bows, I recommend "stickbow.com" and "tradgang.com". So many good, knowledgeable traditional guys on both sites.
