Absolutely to both questions.
As far as wood goes, besides any minor fitting appropriate for barrel contour, etc. (which would be the same for later NEF/H&R stuff) every thing cross matches.
The Shikari came with a "cleaning rod" which is the same collapsing item as their ram rod save the (useless) eye-type patch jag on its end.
And Yes, it hung from the same ramrod thimble attached to the barrel as the Huntsmans wore.
The wood and other appearances of the Shikari 28" barrel model (.45-70) and Huntsmans (.45, .58 &12ga.) of that era were indistinguishable.
The shorter bbl. Shikaris were chambered .44 mag. Actual bbl. length on those I don't this moment recall, but they wore a thimble also I believe.