The incident was one of just 12 dealt with by the service during the late shift yesterday.
Logs shared by the service today reveal the boy turned up to Scarborough Fire Station just before 7pm after he was unable to release himself.
Crews used smalls tools to free his hands from the cuffs.
Meanwhile, a crew from Bedale was called out to reports of a diesel leak at a property in Bullamoor Road, Northallerton, at around 5.45pm.
The fire service reported the leak appeared to be underground, but up to 600 litres of diesel may have leaked into the water course.
At the same time, the crew from Northallerton was dispatched to the A19 near the Cleveland Tontinue where an HGV and tanker carrying carbon dioxide had collided.
No action was needed by firefighters as there was no gas leak and nobody was trapped.
Other calls included a bin fire in the layby near the entrance to Skipton Golf Club and a pile of leaves on fire in the entrance to a disused toilet in the Kirkgate area of Sherburn in Elmet.