that's because there are no directories post 1894
There are Electoral registers, incomplete, held by manx Museum - they are not digitised nor on-line thus personal research needed.

The Douglas rate books (again need personal research but I've never used these so not sure available to public or where they are currently held) should indicate when he took over the premises (in 1881 used by a dressmaker), I've seen the Peel rate books and they contain this sort of info - Wellington street now lies underneath the carpark attached to Marks and Spencers - I wonder where the electric power to do electro-plating came from - presumeably a gas engine driving a dynamo.