Which word is correct in this sentence? (signing/signature)

Either word is correct here, but 'signing' would be the more commonly used word.

Signature is more commonly used to refer to the product of signing one's name than the act of signing itself. It is defined by Wiktionary as

1. A person's name, written by that person, used as identification or to signify approval of accompanying material, such as a legal contract.
2. An act of signing one's name; an act of producing a signature.

The Cambridge Dictionary definition for Signature meaning the

the act of signing something

notes it as formal. It would still be correct to use it in this instance, but it is a less common usage.

To provide some evidence of this usage of signature being less common than signing, I did some Google searches.

A Google search for "signature of the Magna Carta" provides about 15,500 results while "signing of the Magna Carta" provides about 99,200. Below is a table with results for the same Google searches with some other historical documents.

Document that was signed        Signature    Signing
Magna Carta                     15,500       99,200
Declaration of Independence     186,000      713,000
Treaty of Paris                 81,000       236,000
Treaty of Versailles            41,600       168,000
Buttonwood Agreement            4            1,850

As you can see, signing is much more common than signature in this usage.