i can totally understand his excitement/nervousness/apprehension, etc. and it is not unheard of that you could, at 39 weeks, be told, "oh yeah, you're dilated enough/time to get this baby out, etc., but if this is a first baby, it is more likely that you won't be told this.
but i trust your instincts that your fiance should stay at work and not attend this one. after all, he has a child on the way (and almost here!) and in this economy, keeping a solid steady job, and impressing the boss to boot, is no small matter.
take your cell phone, tell him to have his on vibrate and in his pocket, and that you will call him from the examining room with a real-time update. also, remind him that wait-times for appointments at the obstetrician's office are unpredictable, and maybe even offer that if he wants he should meet you there AFTER work and you will do what you can to delay the appointment (let a few other women go before you), assuming that it is not the last scheduled appt time. perhaps it will be a busy day at the ob's office, and he'll still get to attend the appointment. But, I'm with you. Tell him how much you appreciate his support and excitement, but that you and the baby have other needs from him as well, particularly, that his job is steady and solid, and that it would give you peace of mind to know that he's taking care of that department.
Have a wonderful labor and delivery, whenever it is, and enjoy the family you are creating with this thoughtful man!