Can a Kenku communicate with sign language?

The description for the Kenku race (Giger’s, Kenku) includes this statement:

You can read and write Common and Auran, but you can speak only by using your Mimicry trait.

In the Kenku origin tale, the description further explains that:

… to ensure that the kenku could never divulge any secrets, their master took away their voices.

and

Although unable to speak in their own voices, kenku can perfectly mimic any sound they hear, from a halfling’s voice to the noise of rocks clattering down a hillside. However, kenku cannot create new sounds and can communicate only by using sounds they have heard. Most kenku use a combination of overheard phrases and sound effects to convey their ideas and thoughts.

These quotes are from Giger’s, as I don’t currently have access to Volo’s guide. As I recall Volo’s has a very similar (same?) description of the playable Kenku race. Regardless, all Kenku descriptions include the same limitation on speaking: You can’t do it except by mimicry.

The Kenku have a voice, but it seems they don’t have the ability to vocalize their own words, they have no voice of their own. However, they can form their own words because they can write common and auran, so they can form their own words in writing (right?). The mimicry trait is clearly for speaking only.

As SL is neither vocalized nor written, I would like to know:

Can a Kenku learn sign language and use it to communicate without mimicry?