followed with ‘I wasn’t aware is so important to you. I didn’t want to insult you and if you felt so, I apologize. The word fuck is one I use very often, but I’ll try to control myself around you’
Note I didn’t insult the coworker (no fuck you or fuck off), but simply said ‘fuck’ out loud due to a job error.
is it an office. if so the apology should be more about your behavior in a professional setting not just around one person. If its blue collar it might apply if members of the public are around.