Shakespeare calls for hautboys. How did he pronounce the word, more than 500 years after Hastings (think of it!)? ohBWHA? ohBOYZ? Or what?
/ˈəʊbɔɪ/ (oh + boy)
I have no direct information, but let's reason this out. The most modern pronunciation, as recorded in current British dictionaries, is /ˈəʊbɔɪ/ (hoe + boy), with the first syllabe being the same as that of oboe (/ˈəʊbəʊ/), apart from the initial h. This matches the pronunciation of other words or expressions from French beginning with haut: haut monde, haute couture, hauteur, … It actually matches the French (and Middle French) pronunciation of haut.
The second syllable, which sounds like boy, is also quite close to how Middle French boy sounded like (and very unlike the Modern French bois, /bwɑ/, like in bwana).
Now, would it be pronunced the same in Shakespearean times? Given that it came from Middle French, and in its most modern form still sounds like Middle French, I don't think it evolved in-between (and then went back to the French-like pronunciation). Also, the hits I could find for words of Middle French origin in Pronouncing Shakespeare's words: a guide from A to Zounds (like this hit) all seem to indicate pronunciations rather close to the Middle French.
Furthermore, etymonline says of hautboy that it is “frequently nativized as hoboy”. It seems to me that this support the pronunciation I put forth above.
Depending on whether you're pronouncing it the US English or British English way, it looks like this word may be pronounced any of the following ways:
For the record, pronunciation #3 is the closest of the three in pronouncing the 'haut' part of the word the same way as the French do ('haut' comes from the French 'haut', meaning 'high').
Shakespeare is obviously more likely to have pronounced it the (modern) British way; either #2 or #3.