Jeff - I have a '99 700lx same exact hull as yours, don't have a picture, but YES you can mount a transom transducer on the 700lx. Which fishfinder are you putting on, only reason I ask is if you are doing a Side Imaging Humminbird (assume its the same for the HDS from lorrance) you'll need to mount it differently (but still on the transom) due to the need for a clear shot on both sides of the boat.
Basically, you want to mount it on the first step below the back of the transom close to the outside, if you look at the back of the boat you'll notice the transom goes down then there is a 90 degree turn IN towards the front of the boat then it comes down again and there is a flat area perpendicular before it steps down again. That is where you mount the transducer to the hull with the bottom of the transducer parallel to the garage floor just below that 'step' so it is in the water when the boat is running on plane. Remember anytime you DRILL into the boat, make sure you mask the holes first to minimize cracks in the gelcoat, after drilling but before putting the screws in fill the holes with 3M marine sealant so that all holes are water tight.
Let me know if that makes sense. I've not heard of any of the Nitro hulls that can not mount a transom transducer.