Book source for linen smoothers with handles:
Martin Biddle - Object and Economy in Medieval Winchester
https://www.google.co.uk/books/edition/Object_and_Economy_in_Medieval_Wincheste/KRdVEQAAQBAJ?hl=en&gbpv=1&dq=linen+smoother+charleston&pg=PA240&printsec=frontcoverSee page 240 and onto page 241 Chapter
viii - Slickstones, R.J. Charleston'
In the sixteenth century these smoothers seem to have acquired a vertical handle, giving them a mushroom shape, and they were certainly made in England at a number of glasshouses. 5.'
Note 5. gives 4 place sources for these including Woodchester (Glos): Daniels 1950, 9-10, Pls 3 and 4.
Earlier in the chapter it talks about slickstones being used in Scandinavia up to the 19th century. To me this, and other evidence (e.g. the conversation in Scotland taking place at the end 19th century re the slickstone being in the old household) seems to refer to those without handles.
I can't find any sources that demonstrate slickstones with handles were being used that late on (19th century), or at any point used as linen smoothers at all actually.