Hi again, Andrew. Thank you for sharing the opening of your book and I hope you don't feel that I have presurised you into posting.
Beginnings are always difficult and so crucial to get right. I think you need to consider your story arc and ask if the decapitation is the inciting incident. I would guess that it almost certainly is and so it should be at, or very near to, the beginning. Thus far the structure is fine but towards the end of the piece you give us what amounts to a preamble - "It has often been thought ..." I think, as you have suggested, this fits better (after a bit of tinkering) at the beginning; to lead the reader's thoughts towards what is coming. It doesn't need to be a prologue as such, just an opening paragraph and then follow it with the date to indicate that the real action us about to start.
I felt that you didn't introduce the characters well. You refer to Daniel at the beginning then we discover he is Cross which is a bit confusing. The assassin, does he have a name? Perhaps have Daniel say "So you found me then, XXXXXXX". His first introduction is as a "young man"
Also, using bold when the assassin speaks is a bit of a ripoff from Terry Pratchet's capitalisation of Death's remarks.
Much of the extract is telling rather than showing. Increasing the amount of dialogue would help and some of the description need tightening - do you need to mention the mild electric shock for example.
You start in Daniel's POV. This has to change after his decapitation - obviously (or, thinking mischievously, perhaps not! Bring a whole new meaning to a 'talking head'). Maybe have the assassin watching Daniel by the harbour wall and then approaching him. The rest then follows from the assassin's POV and you avoid the awkward change part way through.
Lastly, I felt there were too many adverbs. Taking words ending with ly, in 841 words, there were 12; 3 in the first paragraph. Try to strengthen verbs to avoid the need to qualify with an adverb. For example, in the first paragraph, try "the waves susurrated against the harbour wall", and omit suddenly and briefly - they add nothing.
Now for the good bit; I want to know more. There are so many questions at the end that I want to turn the page and find out the answers. This is the start of an intriguing tale and I wish you the very best of luck with it.