That quaint “yee” was actually pronounced “the.” The confusion with the “y” sound began because Medieval scribes had to make some difficult choices:
Medieval English thus contained a variety of signs for the sound ‘th’ – the digraph ‘TH’, the thorn, and the eth (or thok). Scribes ended up using a mixture of these, although some tried to make a distinction between those used for a voiced ‘th’ sound and the signs used for a voiceless ‘th’. As a result, reading medieval texts today can be enormously confusing. Is that a ‘y’? Is it a ‘p’? Or a ‘th’? The problem is compounded by the inclusion of yet another runic sign which made it into Medieval English – the wen, a symbol that looks very like a thorn, except that the triangular portion sits even higher, giving it a strong look of an angular ‘p’.
The thorn symbol persists in UTF-8 character sets – Þ – but was lacking in early typesetting.
There was no thorn sign in the printing fonts, as they were usually cast outside of England. So, since the sign for thorn slightly resembled the lower-case ‘y’, that’s what was substituted.
In screenwriting, you’re always balancing accuracy with expectation. Thus, the warriors of Sparta speak English with British accents — because anything else would feel strange to the audience.
But in portraying your characters’ world, you have wide latitude. If you’re writing a broad comedy set in Medieval times, go ahead and ye it up. Put it Zapf Chancery if it helps sell the joke.
But in more serious films, I’d love to see written English portrayed more as it would have been in the time. That is, really odd to modern eyes, filled with runic characters and odd constructions.