How can one "smoke ship's?"
Solution 1:
Here’s a description of “ship’s tobacco” by a turn-of-the-century chaplain in the Royal Navy:
Most people who take any interest in “ships and the sea” have heard of “ship’s tobacco.” It is indeed difficult to imagine a sailor who doesn’t smoke, though, as a matter of fact, there are a considerable number of non-smokers amongst us, and a still larger number who prefer trifling with a cigarette to an honest pipe of “ship’s”. Some of my readers may have seen our Navy tobacco as prepared by the men themselves, a solid block covered with canvas, round which spun-yarn is wound in such a way as to make it like a miniature torpedo. The process of preparation is something of this kind : The tobacco, being served out in the leaf, is first of all wetted, and wrapped up in a bit of ship’s canvas ; then a line of tarry cord is fastened up at some convenient spot on the deck, and, by a mystic process which I never quite followed, the sailor, astride across this line, works it round the canvas tightly, until the latter is completely covered and the tobacco pressed into the orthodox form. In a short time it is ready for use, and may be sliced off or shredded off with the sailor’s jack-knife as required. The strength or mildness of the tobacco depends a good deal on the amount of saltpeter used to preserve the leaves. Those who like a “full” flavor are careful to retain as much of the saltpeter as possible ; a “medium” flavor is obtained by judicious washing ; while the “mild” form may be reached by a thorough cleansing of the leaves. As smoked by the bluejackets it is decidedly “full.”
— Rev. George Goodenough, RN, The Handy Man Afloat and Ashore, 1901, p. 157.
There’s a deal more about “ship’s” at the link.
Solution 2:
It appears to not be a phrase, but a proper noun:
Sherlock asks "You don't mind strong tobacco?"
But Watson's response doesn't explicitly answer Yes or No. Instead, he replies, "[Not only do I not mind the smell, I myself frequently create such an aroma.] I always smoke "ship's" tobacco, myself [a style of preparing tobacco which is described as the opposite of "mild"]"
Just a possible typographical error. No punctuation, but a * or footnote would be helpful.