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Has anyone had glass shrimp in with their pygmy corys? Do you think I should get the shrimp out of there or are the corys safe? Would the corys be okay with cherry shrimp?

Pygmy cories will be absolutely fine with the shrimps - cories are generally very peaceful & the largest aquatic creatures they'll eat are bloodworms etc Their mouhs are not really equipped to handle shrimps!

Actually, I was worried about it the other way around. I heard that ghost shrimp will try to catch and eat fish.

It depends upon exactly which species we are referring to - most "shrimps" are ok some lobsters & crayfish definately attack fish but a latin name will allow us to give an exact answer.

I have no idea. They were just called ghost shrimp, sold as feeders. So I got 6 of them instead of paying $2 each for cherry shrimp. They're maybe just over an inch.

There are many species of small shrimps that are sold as "glassshrimps" Make sure it is not Macrobrachium lanchesteri http://akvaforum.no/dyr.cfm?id=1129&tab=3&image=1182 because they are very predatory at night. Thet look very harmless, but they are one of the meanest shrimps I have ever kept.

Neocaridina shrimps (like cherry shrimp)will be excellent for a corydoras tank. I keep Neocaridina species in almost all my fish tanks.

The problem is that "glass shrimp" can be almost anything, literally dozens of species of 3-4 genera go by that name.
Species of the genus Macrobrachium (long-armed shrimp) are as a rule NOT safe with fish, many of them are specialized fish predators.

The Glass Shrimp sold in the USA are fish safe.
They may eat Corydoras larvae, however.
The red cherry shrimp are totally safe, even with Corydoras eggs and larvae.
I keep RCS with my breeding C. hastatus and C. habrosus.

The Glass Shrimp sold in the USA are fish safe.

That's a relief because they all look the same to me! I'll only keep the cherry shrimp in my corys' tank and maybe I'll have some cherrys breeding too.