Hi David,
There is a Louis H Cowell listed on the 1881 Census as a 5 year old.(Sometimes ages were wrongly put down on the census). He is listed as living at 23 Bigwell Street, Onchan. Could this be the one? You say he was illegitimate well would he still be using his fathers name of Cowell or his mothers maiden name? Let me know and I'll see what else I can find. Incidentally my grandfather, great grandfather and gg grandfather and my ggg grandfather were all William Cowell.
Sandy Jones(Nee Cowell)