Syringes are probably overkill. Go to your LHS and get some of the CA tip extenders. They're about 1 1/2 inches long and give you good control. For the hinge, cut the covering and make a little rectangle of wood around the hinge slot. Maybe 1/8 wide total and about 1/4" longer than the length of the slot. Do this for both sides. Seal the remaining covering very well.

When you put the glue on, the wood and the slot will wick the CA in. If you are getting it on the covering, you are putting too much on. A few drops on each side is plenty. Hope this helps, Chuck