Would "The explicit personality modification would just affect your fear of death" be an acceptable formulation?
In which case I think my original lobotomy-comparison would be relevant again. If I'd still be "allowed" to update my beliefs, there would be landslide changes originating from the "fear of death removed" change, whether we refer to just the emotion or to our drive of avoiding death. In both of which the former "I" would cease to exist, via lobotomy or via unrecognizable personality.
If someone transplanted a belief of "I can actually fly" into your personality, and an observer compared your actions prior to that belief, and following that belief, don't you think the differences would be so profound as to belie any kind of "personality is pretty much unchanged, other than that" statement?
If you actually believe you can fly, you would simply jump out of a window (at least if noone's looking). After all, you can fly!
Same with the fear of death.
(You could argue that just the emotion gets removed, not your reasoning about death. In which case you would know that dying would forever remove you from your loved ones. However, while you don't fear death (by fiat), you would fear losing your loved ones -- "care about the same things you care about now" -- which would necessarily drive you to avoid dying out of fear. So a scenario in which only your death-related emotions are affected, not your reasoning apparatus, wouldn't change much of anything:
Fear of death as it is is often conferred fear from other things. If you were, however, to disallow any fear (of e.g. losing your loved ones) from also applying to your own death, your emotional makeup wouldn't only be recognizable as (your former) "you", it might barely be recognizable as human.
What would it mean not to fear death but to know all the things, future activities, encounters lost to you if you die? How would you be allowed any feelings about anything period, lest they also transfer to death? A whole lot of reprogramming would be required just to make the "remove fear of death" scenario coherent, even as a hypothetical. I must be missing something.)
Do I understand you correctly that a sapient being with a knowingly finite lifespan must necessarily fear death or (accidentally) suicide? If so, that's a pretty sweeping statement and I can think of several counterexamples.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.