Hi Viv , there are two possibilities :

From Lawsons site,

Alfred to Thomas William Shimmins and Elinor Kelly 18/8/1883 , Malew.

Alfred Ernest to Thomas Walter Shimmins & Margaret A Leece , 30/8/1889 , Douglas.

Could not find Alfred on 1891 & 1901 census , no Burial on Lawsons , but on IGI shows death as 19/5/1887 , aged 3.

So this means Alfred Ernest is your man. Found Thomas Walter , Margaret and Alfred Ernest on 1891 census in Douglas , but by 1901 census Thomas Walter is not there.
On Lawsons burials found Thomas Walter Shimmin buried Arbory 11/4/1900 aged 40.
Searched A Manx Notebook for Thomas Walter Shimmin as an Auctioneer , as it has a lot of Directories , but no sign of him.
No apparent will for T W S

Good Luck
David Dwyer