I've been looking at Edward Wisemans born in England between 1871 and 1881. There were none born in Scotland during that period.
14 Edward Wisemans are in the FreeBMD index of births. Of these, 6 died before 1881. There was another one who died in infancy, but whose birth is not in the index. The remaining eight, plus two whose births are not in the index, are all in the 1881 census.
1. Born Brentford, 1872/Q1/ in London aged 9
2. Born unknown 1872/3, in London aged 8
3. Born Wetherby 1873/Q3, in Yorkshire aged 7
4. Born Huddersfield 1874/Q1, in Yorkshire aged 7
5. Born Bramley 1875/Q3, in Yorkshire aged 5
6. Born Whitechapel 1876/Q4, in London aged 4
7. Born unknown 1877/8, in Yorkshire aged 3
8. Born Chelsea 1878/Q3, in London aged 2
9. Born Swaffham 1878//Q4, in Norfolk aged 2
10. Born Stockton 1879/Q2, in County Durham aged 2
Assuming that your Edward's date of birth is between 1875 (per ship's passenger list) and 1879 (age in 1911 census) you have six possibles.
The 1901 census lists 7 EWs of this age who are probably as follows
No 2 in London, aged 28, fruiterer, greengrocer and coal merchant
No 3 in Yorkshire, aged 28, grocer's assistant
No 4 in Yorkshire, aged 27, tailor
No 5 in London, aged 25, factory stoker
No 6 in London, aged 25, carman
No 8 in London, aged 22, .... assistant
No 10 in Stockton, aged 22, baker.
No sign of No 1, No 7 or No 9. There are no deaths in the English or Scottish indexes which would account for them and none of them is in Scotland. As your soldier was aged 18 in the 1891 census, he would be No 1 or No 2.
Looking at the occupations seems to strengthen the likelihood that No 8 is indeed yours.
HTH