cornsnake problem

I've had cornsnakes for 3 years now and this years clutches came out about 2 weeks ago. Got some nice snakes but there were two in one of the clutches that never lost their umbilical cords. The area where the cord attaches is starting to become swollen and I need to know if i should cut the cords off. I have never had this problem before.
Thanks

Please if you can help, reply.

My thought is that an infection, or a possible intestinal problem, is likely.
You need to take them to a reptile vet.

BTW Are the cords still wet or are they dry?

Its wet and very swollen

Normally when this happens you can place the snake on a clean, damp paper towel and it will come off on it's own after a few days. If the umbilical cord is still attached after two weeks there may be an infection. Can you post a photo of what it looks like now?
Does the snake appear healthy otherwise? Has it had it's 1st shed yet?

One of the babies I had to put out of its misery. An expert I know, told me that gnats had laid eggs inside the snake. The other snake I will try to get a picture of later. And I will try the wet paper towel.
Thanks.

Normally, if a hatchling still has its cord attached, after leaving its egg, they are, immediately, placed in an enclosure/deli with damp paper towel lining the bottom. The cord usually falls off day/s later or on up to a week later.

With your remaining one still having a moist (and swollen) cord, it is good that you will put damp paper towel lining in its enclosure. Make sure the PT lining remains extremely clean.
You could also swab some iodine/betadine solution to the cord, etc. Dilute 1 part iodine (10%), to 9 or 10 parts water, first.

That said, I suspect infection. So, unless you have antiobiotics (and know the dosage) or take the hatchling to a vet, I fear that the outcome will not be a good one.