After the restart, the game settled into a pattern where Switzerland enjoyed plenty more possession but Northern Ireland created the better opportunities.
The best of them fell to goalscorer Price only minutes into the half.
Shea Charles' teasing delivery was perfectly weighted across the goal but Price could not make the desired connection from six yards and the ball spun over the bar.
Brodie Spencer did have to be alert to block debutant Isaac Schmidt's strike on goal, but at the other end Ethan Galbraith put an effort just wide.
Forward Donley, whose international transfer from the England under-age set-up was finalised this week, was introduced in place of Smyth in the 58th minute.
With a quarter of an hour to go, the 20-year-old, on loan at Leyton Orient, went close with a deft header that produced a flying one-handed save from Kobel.
Pierce Charles had to be equally alert soon after to deny Andi Zeqiri who had directed his fellow substitute Alvyn Sanches' cross towards goal, but neither side went any closer to finding a winner.