I understand now, no need for a pic.
If you can find any of the crosshair to get an idea of the diameter of what you need, that will help. And what are they made from? I have no idea as to what illuminated crosshairs might be made from, maybe thin mono fiber>?.
Basically you need to glue on two new crosshairs which isn't hard. What I do is open up a small vice just a little smaller than the ring so that I can lay the crosshair ring across the open jaws on top. Or whatever works.
Next you need two pieces of crosshair about 5" - 6" long, two small clamps to use as weights when attached to each end of the crosshair material. I use those clamps that squeeze together with rubber jaws. Clamp one to each end of the crosshair material and hang them on each side of the ring. Center the crosshair and allow the clamp's weight to pull the crosshair tight. Now place a small amount of good (thin) adhesive where the crosshair touches the ring. Allow to dry, cut of extra crosshair material and clamps and do the other one.
The material that you use will depend on what yours was. If it's just thin wire there's a few things that might work depending on how thin it has to be. I have used one wire from a small strand of real fine copper wire. I used one of the small wires from a computer microphone/headset thing that I never used. There was six small coated coppers wires in it. Remove the insulation and then get one of the small wires free from the strand. These are thin but many times not thin enough. A human hair will work, look for someone with fine hair and pluck out a few. I've heard that you can strip down a piece of dental floss to one fine piece. Spider web.