The Cook chronology by Paul Capper gives not only dates but days of the week as well. However I'm not sure that their calculation took into account the change from the Julian Calendar to the Gregorian calendar.
Great Britain adopted the Gregorian Calendar on 3rd September 1752, which became 14th September.
This led to riots with people wanting their lost eleven days! It is also the reason why the British Budget Day is the 6th April; it used to be on the Quarter Day, i.e. 28th March but because the king had lost eleven day's taxes that year the financial year was extended, and it has remained so ever since.
The Julian Calendar was named after Julius Caesar and modified by Augustus as being 365 and a quarter days in the year. This was 11 minutes short of the astronomical year.
Pope Gregory amended the calendar to adjust for this shortfall but over a period of centuries the time difference became days.
Russia did not adopt the Gregorian Calendar until 1917, so it is possible to obtain postal history material which appears to have arrived before it was sent!
I hope this is of some use. Of course it doesn't really affect J.C. on his voyages but it must have been interesting to see how a cosmetic change to the calendar affected the masses, especially when most of them were illiterate and innumerate!
I suppose J.C. took it in his stride!
Originally published in Cook's Log, page 425, volume 9, number 1 (1986).