All that can presently (March 2021) be gleaned about Johnny Dwyer
from sheet music covers and by Internet searching is that he has 2 works published between in 1894.
The Music Hall Guild
webpage Resting shows Johnny Dwyer's portrait on the left and describes him as a "Comedian and Singer" interred at the Streatham Park Cemetery.
Surfers are welcome to contribute any further information about this composer/singer.