I looked into this for another thread, and it seems that the answer is no. The noise comes from a speaker in the instrument cluster, and there are no coding changes for the volume.
You could probably go all Rambo on it and pull the cluster and try to muffle it somehow if you can find the speaker, but I really recommend not doing that.
For entertainment, here's a link I posted on the other thread that shows it could be worse...
Changing turn indicator sound in a Mitsubishi Lancer/Evo X - YouTube