So it's not necessarily true that you couldn't do this without impacting fertility or masculinity, but it is true that you'd have to work pretty hard at it and it might bring some unfortunate trade-offs alongside. Effectively, you're trying to disconnect a secondary sex trait from the cascade of sexual development cues and break the regulatory relationship between the trait and your male birds.
If I was going to try this, I'd look long and hard at Sebrights, which already exist as a breed that has accomplished a similar disconnection between "male-ness" and a common secondary sex trait in chickens (in their case, feathering). What you're trying to do is break the regulatory relationship between vocalization (well, motivation to vocalize) and sexual development in a particular direction, and that's exactly what Sebrights have achieved with hen feathering. I don't have the breed knowledge myself with Sebrights to recall how hard the hen feathering was to achieve or how aggressively the breed was originally selected, though.