First and foremost, I want to say how very sorry I am that you learned your father had taken his own life only after obtaining a copy of his death certificate as that was undoubtedly a most unwelcome and unexpected shock for you.
Should you decide to make contact with your half-siblings, I've come up with an alternative to the 'I'm the relative you may not have known you have' approach.
Do you share the same surname as your half-brothers? If so, and if your surname is now different to that of your half-siblings, you could make an oblique approach by asking one of them if they know of a 'your christian name/their surname' who you believe may be a relative of and see what response you get before you proceed further.
Alternatively, do you have a friend or other third party that you could entrust to make this enquiry for you?
Given that your father has been deceased for some 20 years I doubt that, even if they are currently unaware of your existence, news of you can in any way turn their lives upside down as it would seem that you are the product of a relationship that your father had back in the day and well before they were conceived.
It may be that one or both of them will be pleased to know as much as you do about their father's life before he met their mother(s) and they will welcome another addition to their biological family.
However, do be prepared for the fact that they may not want to know you or to have any communication with you. In this event, I hope you won't take it as personal rejection and will view it as their having unresolved issues to do with the circumstances of your father's unnatural and premature death.
If this should prove to be the case, simply pass on your contact details and let him/them know that you will always respond to any future communication from them.
There is another possible scenario wherein neither of your siblings are people that you would wish to know and, for this reason, I would suggest that you proceed with caution and don't go overboard if they appear to be wholly welcoming until such time as you are confident that you have more in common than a few pints of shared blood.
I fully understand your hesitancy but I believe that this is one of those occasions where you won't feel at wholly at peace until you've reached out to your half-siblings and, IMO, you have nothing to fear by doing so such a very long time after the death of your father.
I hope it goes well for you and that you'll come back with an update in due course.