The OED has an excellent discussion under Chirurgeon and Surgeon. The earliest variant given for chirurgeon is cirurgian in 1297. Apparently at some point in or after the Renaissance they got the bright idea that they were supposed to start the word with "ch", with 1535 the earliest citation in the OED. Still later they decided to pronounce the "ch" after the Greek. But they both go back to the Old French cirurgien/serurgien. And starting with an "s" goes back to the early 14th. c..
Different MS. of Chaucer's Melibeus give as indifferent spellings of the same word: sirurgien/surgien/surgeen/surgeane. So they're swallowing the second syllable quite early.
And when it is spelled with a "cir" it must pronounced as in circle, otherwise the alternate spellings don't make sense. Now, very late in the Middle Ages, you do see "ch" as an alternative beginning. But it's a soft "ch", not a hard one. (Remember, this is coming out of French, so think of champagne)
The medieval pronunciation seems to have been more like Sir Urchin. Or, more precisely, sir-ur-jyen. By the fourteenth century it seems to have been fairly common to pronounce it surgeon. The radical change in pronunciation seems to have happened after, and probably because, the various variants of the spelling cirurgien had fallen out of ordinary use.
I suppose a similar process would happen if people stopped using Worcestershire sauce, and the term only survived in historical novels. 23rd century reenactors would probably insist on pronouncing every syllable, and using a hard "c" on the basis of original word roots.