Yes, both the beautiful fire shrimp (Lysmata debelius) and a wily, old ghost shrimp that has been elusive enough to escape being eaten could potentially pose a threat to newborn seahorses. But, in your case, the risk they pose to the newborns is really very slight. Allow me to elaborate.
Clara and Snoopy are Sunbursts (Hippocampus erectus), and the offspring they produce will undergo a brief pelagic phase of development, which means that the newborns will head for the top of the tank immediately after birth. All of the babies will congregate at the top of the aquarium, safely out of reach of the shrimp, which will be hiding out amidst the rockwork and coral caves and overhangs at the bottom of the tank.
Now, it’s a sure thing that your ghost shrimp survivor — that has managed to remain uneaten all this while by carefully concealing itself and staying well out of harm’s way — is not going to leave his hiding place and head up to the surface where the babies are because that would be a suicidal gesture on its part. The ghost shrimp’s survival instincts will keep him well concealed at the bottom of the tank until you have had a chance to retrieve the newborns and transfer them safely to your nursery tank.
The fire shrimp is likewise unlikely to pursue the babies to the top of the tank and leave itself completely exposed while it does so. As you know, Lysmata debelius is very shy and reclusive in nature, and prefers the shelter of crevices and overhanging ledges rather than the open water in the aquarium. Now, if you had a Scarlet cleaner shrimp (Lysmata amboinensis), which is much bolder, more active, and more aggressive than fire shrimp, then the newborns would be in real danger. A brazen Scarlet cleaner shrimp would not hesitate to dart up to the surface, snare one or two or more of the newborns, and then dash back down to the substrate to feed on its catch. It wouldn’t take a hungry Scarlet cleaner shrimp (L. amboinensis) long to decimate the babies, but your fire shrimp is a very different animal. The fire shrimp could be a threat to the babies if they venture down to the bottom of the tank, but it will be several days at least before the Sunburst babies are ready to settle out and orient to the bottom.
Both the ghost shrimp and the fire shrimp could present a serious threat to benthic seahorse babies, but they are nothing for you to be overly concerned about, Carolina, because your Sunburst babies will all be gathering at the top of the tank, well out of danger.
However, because they are going to be hugging the surface, the babies could certainly be at risk from being "eaten" by the filtration system for your aquarium. They could sucked over an overflow and wind up down in the sump, for example, or they could get drawn into the intake from an external filter, so you may want to screen off the overflow or filter intakes until you are certain whether or not Snoopy is pregnant at the moment.
Plastic window screen will work well for this purpose. The plastic window screen is easy to cut into the necessary size and shape, and the mesh is small enough to keep out pesky flies and mosquitoes, which means it will also restrain newborn Sunbursts. But at the same time, the plastic window screen mesh is large enough to allow water to easily flow-through it and to resist clogging, so it won’t harm the pumps or filters or cause the tank to overflow by obstructing the overflow box.
Best of luck with Clara and Snoopy, Carolina!