The barrister, who's been accused of abuse at camps in the UK, is reported to have written to parents of children attending Zambesi Holidays in Zimbabwe to explain the punishment he would give to unruly pupils.
It's claimed in the letter he mentions using a table tennis bat as well as what is described as a 'Jokari' bat for more serious offences.
Smyth, who has refused to respond to allegations, is also said to have written about showering with boys to create a family atmosphere.
The letter, which has been seen by the Sunday Telegraph, says: "I never cane the boys, but I do whack them with a table tennis bat when necessary.
"I am determined that we should avoid a school atmosphere as far as possible. I am not a schoolmaster; I try instead to be something of a father figure to the camp, encouraging the younger leaders to care for their campers in the way the best of big brothers should.
"To this end we use Christian names all round, the younger leaders sleep in the dormitories with their campers, and we all (including myself from time to time) have our showers with the boys."
Alleged abuse, attributed to Smyth during his time at Iwerne camps in the UK, was highlighted in a report by Channel 4 last week.
The Archbishop of Canterbury Justin Welby, who also worked at the camps, has insisted he was "completely unaware" of the allegations after the Church issued an apology over its handling of the claims.