My much loved relative killed herself a few years ago.
In my head, I use "suicide" most often - not out loud as that upsets her very closest family members who never wanted the word suicide used. Amongst our family we use "took her life/took her own life/ended her life". Sometimes killed herself, that's how it was broken to me...that's the most painful way I describe it I think...there's a visceral response for me. Very privately we might use the verb of what exactly she did to end her life...obviously not this but substitute the appropriate verb, "i.e L went to the shops" but we would never ever discuss the method used outside of immediate family. If you know and if someone asks what they did to kill themselves, please never ever share that information. My preferred term is "ended her life"...as that sums up her background/suffering/the hope she is free from her years of pain now. It feels more gentle as ridiculous as that sounds, and befitting of what she did and what her intentions were...but I'm a few years down the line and have "arrived" at that.
At her funeral, the celebrant passed on to the congregation that her children wished that when we spoke about L, we refrained from using the term "committed suicide" as this felt like an outdated term, which carried the sense of having committed a crime and they didn't want their mother to be remembered that way. The celebrant said, if we must, we might choose to say that L took her own life or ended her life and that this would be what her children preferred and felt was appropriate.
In your shoes, I'd say something like, "I'm sorry to share the news that Fred Smith died suddenly yesterday, having taken his life.The Smith family are understandably devastated and requested I share the news on their behalf. I will share details of the funeral in due course. "
Also...I am sorry that you are in this position and that someone you know has died in this way, before their time. Very sad and difficult. It's kind of you to do this for the family, but make sure you can access support if you need to as well.