Greenslade is among six players in the men’s singles who remain unbeaten after the opening two matches.
He saw off Olle Backgren from Sweden 17-2, 8-2.
Also with 100% records are England’s Harry Goodwin, former event winner Shannon McIllroy (New Zealand), Ray Pearce (Australia), Izzat Shameer Dzulkeple (Malaysia), and Clive McGreal (Isle of Man)
In the women’s event, defending champion, Scotland’s Julie Forrest was beaten by Jersey’s Lindsey Greechan, a former world Under 25 champion.
Guernsey’s Rose Ogier beat Caroline Whitehead from the Isle of Man 9-4, 5-4.
In the mixed pairs, Guernsey players secured their first victories after a barren opening day.
Alison Merrien is partnering with Sweden’s Olle Backgren from Sweden. They won 16-1, 12-3 scorecard against Irit Grencel and Gabor Foti (Israel and Hungary).
Rose Ogier and Greenslade beat Rahsan and Ozkan Akar (Turkiye) 8-4, 7-3.