What's the barrel profile ? Look on the underside of the barrel, just forward of the fore end, it should be stamped there.
Most common profile is a 3, but they were available from a 1 to a 5, normally.
If there is enough meat left on the barrel, it may be a good candidate for a rebore.
If the barrel is a 1 or 2 size, it is likely to be a small shank, if a 3, probably large shank, but remotely possible that it is small, and over that, probably large shank.
Note the "weasel words". Winchester would make just about anything the customer wanted, on the 1885 action. Winchester made a lot of small shank barrels on the High Wall action.
Small shank barrels are .824"/.825" x 16 v threads per inch.
Large shank barrels are .935" x 16 v threads per inch.
This per Campbell's books "The Winchester Single Shot" and "The Winchester Single Shot Volume II"
Good books, too! Very well written, and a lot of neat info covering the 1885.
Cheers
Trev