Which version of this sentence should I use?

Okay. In my story, a character has neglected to bring a car jack on a long camping trip and unfortunately her van now needs a tyre replacing. Conveniently enough, an alien comes along and elevates it two feet off the ground so she can line up the spare wheel. (Yes, I realise how ridiculous I have made it sound but in the context… I have poetic license, so there.)
Anyway, the point is this alien is not invincible and cannot hold a rickety old van very effectively. At the interval between my character removing the flat tyre and fitting the new one, her companion begins to lose his grip and the van tips toward her. I only tell you this because I have puzzled over a certain sentence for a very long while and I believe some context is in order before you can come to a definite decision. Here is an excerpt:

“Then, for one horrifying moment, the van leaned towards me, quivering. I gasped, unable to move as I watched the buckled metal draw rapidly closer. The only thing which registered in my mind in that single fragment of time was the logo welded onto the tipping door. At some time in its hundred years of life it would have advertised ‘Starwagon’, but due to slow decay it now simply read, quite fittingly, ‘tarwagon’. My first and only emotion, at this moment when death seemed inevitable, was indignation. I’d be the only person in history to die with the word ‘tarwagon’ imprinted into their skull…”

Now the sentence which throws me is the last one. Should it be, “…only person in history to die with the word ‘tarwagon’ imprinted into THEIR skull…” or “…only person in history to die with the word ‘tarwagon’ imprinted into MY skull…”?

Thanks for any help! I can’t come to a decision!
@Amaretta:

Yes, I do rather prefer the sound of “her skull” as opposed to “their skull”… but can “her” be all-encompassing when it comes to population? I know “his” can be used to collectively group people regardless of their gender, but seeing as my character is female it would seem a bit odd to classify her under “his”. I guess my only concern with “her” is that it’s never been used to group males and females together…