The former Middlesex all-rounder, in line to face the Black Caps in the first of three one-day clashes at Ayr on Friday, faced 157 balls and hit 12 boundaries.
Davey then took two wickets and two catches as Somerset built a first-innings lead, but was out for a duck in the second innings as the match headed towards a draw.
New Zealand, meanwhile, completed their business south of the border with an emphatic win over England Lions to clinch a triangular series which also included Sri Lanka A. Yorkshire's Jonny Bairstow hit 77 as England made 255 for eight at Worcester despite three wickets for Matt Henry, but the tourists, who travel to Scotland today, romped to a rain-revised target of 220 with seven wickets and 21 balls to spare.
Hamish Rutherford, the former Ayr overseas amateur, ripped the English bowling apart to hit 95 from just 84 balls with ten fours and two huge sixes. Tom Latham, a former Saltires professional, was unbeaten on 48, smashing the winning runs with a six out of the ground.
Meanwhile, Cricket Scotland officials last night announced that the Murgitroyd T20 Cup finals day will take place this Sunday, the originally scheduled date.
It had been brought forward to August 10 to avoid a clash with Sunday's one-day game between Scotland and New Zealand A but the washout last weeken left organisers no option but to revert to the original date, so three of the four clubs in the semi-finals will be denied the services of key players.
Clydesdale are hardest hit, with Richie Berrington and Majid Haq out of their game with Dumfries.
Craig Wallace, Forfarshire's captain and leading run scorer, and George Munsey of Grange will be absent from the second semi-final.